AP PGECET 2024 Civil Engineering Question Paper is available for download here. Sri Venkateswara University, Tirupati on behalf of APSCHE conducted AP PGECET 2024 Civil Engineering on May 30 in Shift 1 from 9 AM to 11 AM. AP PGECET Question Paper 2024 consists of 120 MCQ-based questions in total carrying 1 mark each to be attempted in the duration of 2 hours.
AP PGECET 2024 Civil Engineering Question Paper with Answer Key PDF
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The elongation of a conical bar of length L under the action of its own weight is ___ that of a prismatic bar of the same length.
A steel cylinder of diameter 100 mm and a copper tube of an outer diameter 200 mm are compressed between the plates of a press. If the ratio of their moduli (steel to copper) is 15/8, what is the ratio of their stresses in steel (\( \sigma_s \)) and copper (\( \sigma_c \))?
In ___ bending, the direction of the neutral axis will not be perpendicular to the plane of bending.
If the thin cylindrical shell having diameter \( D \) and subjected to internal pressure \( p \), the ratio of longitudinal pressure to hoop stress is equal to
The maximum shear stress in a Mohr’s stress circle is equal to
A soil has a discharge velocity of \( 6 \times 10^{-7} \, m/s \) and a void ratio of 0.5. Its seepage velocity is
In an element of a stressed body is under the state of pure shear of 60 N/mm\(^2\), the magnitude of maximum principal stress at that location is
The error in discharge due to error in the measurement of head over a triangular notch is given by:
The torque that produces a twist of one radian in a shaft of unit length is called
A simply supported beam of span \( L \) and constant width \( b \) carries a point load \( W \) at mid span. The depth of the beam required at the mid span to make the beam of uniform strength for maximum extreme fibre stress \( \sigma \) is
What is the degree of redundancy for the given beam?
What is the degree of static indeterminacy for the given truss?
What is the Kinematic Indeterminacy for the given frame without axial deformation?
A simply supported beam of span 4 m subjected to two-point loads of 60 kN and 40 kN at a distance of 1 m from either supports respectively. An equivalent beam of the same span subjected to 50 kN load at the mid span which produces a vertical deflection of 40 mm and 60 mm at distance of 1 m from either supports. Determine the deflection under the load of 50 kN.
A saturated soil mass has a total density of 22 kN/m\(^3\) and a water content of 10%. What is the dry density of the soil?
What is the horizontal thrust at the ends of the arch as shown in the figure?
What is the moment at the joint C shown in the figure below?
What is the shape of the ILD for bending moment at point 'C' of a cantilever beam when the unit load is between C and B as shown in figure?
A beam of span \( L \) and is fixed at both ends. If that beam is subjected to a concentrated load at the middle of the span, what is the fixed end moment at the left end?
Consider a beam which is fixed at end A and simply supported at end B of span \( L \). If the support B settles by an amount \( \delta \), then what is the fixed-end moment (FEM) developed at end A?
Normally, the tensile strength of concrete is aboutof its compressive strength.
In a simply supported reinforced concrete beam, the reinforcement is placed ___ to the neutral axis.
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The section in which concrete is not fully stressed to its maximum permissible value while steel reaches its maximum value, is called ___
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In a beam, the transverse reinforcement is provided at ___ to the span of the slab.
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The minimum size of the reinforcement bar in RCC column is ___
Maximum reinforcement in an RCC beam of dimension b x d shall not exceed ___
Lateral ties in RC columns are provided to resist ___
Maximum longitudinal reinforcement in columns shall not exceed ___
The grade of concrete used for prestressed concrete shall not be less than
The profile of the prestressing steel in prestressed concrete member follows
Which one of the following statements regarding coefficient of consolidation \( C_v \) is correct
Where do you provide bearing stiffeners?
Which of the following is reversible?
Plastic modulus for a circular section of diameter \( d \) is
A cohesionless soil having an angle of shearing resistance of \( \phi \) is standing at a slope of angle \( i \). The factor of safety of the slope is
Plastic analysis must satisfy the following conditions
If the degrees of redundancy for a structure is \( r \), the number of plastic hinges required to convert a stable structure into an unstable mechanism is
Which of the following component has more influence on the mechanical properties of steel?
Negative skin friction in a soil is considered when the pile is constructed through
As per IS 875, where access is not provided except for maintenance, live load on roofs, while designing a truss, in respect of its plan area is adopted as
If a clay has an air content of 38%, its degree of saturation is ___
Effective size of a soil is ___
Toughness Index gives a measure of Shear Strength of soil at ___
If a clay deposit undergoes an ultimate consolidation settlement of 45mm under single drainage condition, the ultimate consolidation settlement of the same clay deposit under double drainage condition will be ___
The shear test conducted for evaluation of shear strength of soft clay is ___
Name the roller best suitable for compaction of Cohesionless soils
At Shrinkage Limit, the soil is ___
The inclination of failure plane with horizontal in passive case behind a Retaining wall with smooth vertical with sand Backfill having angle of shearing resistance of \( ϕ = 30^\circ \) is ___
When retaining wall moves away from the backfill, the pressure exerted on the wall is known as
Corrected Value of Standard Penetration Resistance for overburden (N) in a saturated Silty sand deposit is 23, then the corrected value of N after applying Density correction is ___
A horizontal water jet with a velocity of 10 m/s and cross-sectional area of 10 mm\(^2\) strikes a flat plate held normal to the flow direction. The density of water is 1000 kg/m\(^3\). The total force on the plate due to the jet is
A 1:100 scale model of spillway is to be tested in the laboratory. The discharge in the prototype is 1000 m\(^3\)/s. The discharge to be maintained in the model test is
Find the rate of flow for a rectangular channel 4m wide and a uniform flow depth of 2.0m. The channel is having bed slope as 1 in 100. The Chezy’s constant C is 55.
A body floating in a water is in a stable state of equilibrium if its
The Froude number of flow in a rectangular channel is 0.8. If the depth of flow is 2.5 m, the critical depth is ___
The unit of dynamic viscosity of a fluid
The material that exhibits the different properties in different directions is said to be
The reading of differential manometer of a Venturimeter, placed at 45\(^\circ\) to the horizontal is 14 cm. If the Venturimeter is turned to horizontal position, the manometer reading will be
X-component of velocity in a 2D incompressible flow is given by \( u = x^2 + y^2 \). If Y-component of the velocity is equal to zero in y=0, then the equation for Y is given by
A hydraulic turbine has a discharge of \( 6 \, m^3/s \), when operating under a head of 60 m with a speed of 500 revolutions per minute. If it is to operate under a head of 15 m, for the same discharge, the rotational speed in revolutions per minute will approximately be
Isohyetal method gives accurate mean areal depth of rainfall
In a dam, longitudinal joints are provided with
Depth-Area-Duration curves of precipitation drawn as a
Water present in an artesian aquifer is usually
Hydrograph is a plot of
Pick up the incorrect crop and its harvesting time relation
The optimum depth of kaw-watering for rice crop is
In a super passage
A turbine develops 2512 kW at 240 rpm. The approximate torque in the shaft is
The discharge from weirs without end contractions are measured by
As per IS-875, where access is not provided except for maintenance, live load on roofs, while designing a truss, in respect of its plan area is adopted as
The Stoke's equation giving the terminal settling velocity of a discrete spherical particle is applicable for particle size range of
Which is the effective pH range for aluminum sulfate as coagulant in water treatment?
Which of the following processes/mechanism (most appropriately) are thought to occur in the filtration process used in the water treatment?
When the pH of the chlorinated water is type 5.5, the predominant constituent in the free available chlorine is:
The most appropriate chemical required for the removal of hardness in water due to the presence of calcium sulphate or chloride is
In general, the minimum value of the ratio of BOD to COD for biodegradability of wastewater without acclimatization will be:
The Food to Microorganisms ratio used in the activated sludge process is given by ___ , where \(V\) is the volume of the reactor, \(S_0\) is the influent substrate concentration, \(SRT\) is the solids retention time, \(X\) is the MLSS, and \(Q\) is the rate of inflow of sewage.
The proportional perimeter of a circular sewer section when the sewage is running partially full is ___ .
The incubation period and the temperature used normally for the BOD are estimated in the laboratory as ___ and ___ .
Land sea breeze and Sea land breeze occur on ___ .
Impacts of Air Pollution on plants are ___ .
View Solution
Air pollution adversely affects plant life, leading to symptoms such as chlorosis (yellowing of leaves) and necrosis (death of plant tissue). These symptoms result from toxic compounds in polluted air that damage plant cells, particularly in sensitive species. Quick Tip: When studying the effects of air pollution on plants, focus on identifying symptoms like chlorosis and necrosis, which are key indicators of damage.
When two plates are placed end to end and are jointed by cover plates, the joint is known as ___ .
Hierarchy of options for Integrated Municipal Solid Waste Management are ___ .
Which of the following is not a factor affecting Municipal Solid Waste generation rate ___ .
Municipal Solid Waste generation rate in India is ___ .
Permissible limits of Noise for day time and night time for residential areas in India are ___ .
View Solution
According to noise pollution standards in India, the permissible noise levels for residential areas are **55 dB** during the day and **45 dB** during the night. These limits ensure minimal disturbance to the residents and help maintain a healthier living environment. Quick Tip: Remember that noise pollution is regulated differently based on time of day. Always check local guidelines to adhere to permissible noise levels.
Noise levels can be measured by an instrument called ___ .
View Solution
Noise levels are typically measured using a **sound level meter**. This instrument measures the intensity of sound in decibels (dB) and is widely used for assessing environmental noise pollution. Quick Tip: When assessing noise pollution, a sound level meter is essential for accurately measuring decibel levels.
Auditory effect of Noise is ___ .
View Solution
Long-term exposure to high levels of noise can result in **hearing impairment**. Prolonged noise exposure can damage the auditory system, leading to partial or complete hearing loss. Quick Tip: To protect your hearing, limit exposure to loud noises and use ear protection in high-noise environments.
Noise Pollution can be controlled by the following personal protective equipment ___ .
View Solution
Noise pollution can be controlled by using personal protective equipment such as **ear plugs and ear muffs**. These items help protect the ear from harmful noise exposure, reducing the risk of hearing impairment. Quick Tip: For workers in noisy environments, always ensure proper use of ear plugs and ear muffs to protect hearing.
Locations where traffic on minor road is controlled by stop or give way sign when the minor road crosses a major road, are known as ___ .
For highway alignment, the ideal transition curve is ___ .
The camber provided to Cement Concrete roads in heavy rainfall areas is ___ .
For mixed traffic conditions, super elevation is designed for ___% of design speed.
The 'design gradient' is ___ .
The design speed of road is ___ percentile speed.
‘Narrow Bridge’ sign is ___ sign.
As a forewarned intervention, a traffic rotary is more safe than a signalized intersection, when the proportion of right-turning traffic exceeds ___ .
A Cement concrete pavement slab made of Premixed Quality Concrete should sustain a flexural stress up to ___ .
On roads with divided carriage way with four lanes each and the number of heavy vehicles is considered along each direction, the lane distribution factor is ___ .
Instrument used to set out a right angle from chain line is ___ .
The nature of correction for the sagging of chain is ___ .
The vertical angle made by the magnetic needle in a compass with the horizontal is known as ___ of the needle.
The staff reading taken on a point of known elevation is known as ___ .
The rule used to balance a traverse when the linear and angular measurements are equally precise is known as ___ .
Which of the following sentences are correct as per the uses of flow-duration curves are concerned?
(i) determining dependable flow which information is required for planning of water resources and hydro power projects
(ii) designing a drainage system
(iii) flood control studies
The surveying method which is carried out with bodies of water for the purpose of navigation, water supply and harbor works is called as ___ .
Which of the following is the artificial causes of waterlogging?
The eigenvalues of \( \begin{bmatrix} 0 & -i
i & 0 \end{bmatrix} \) are ___ .
View Solution
To find the eigenvalues of the matrix \( \begin{bmatrix} 0 & -i
i & 0 \end{bmatrix} \), we must solve the characteristic equation: \[ det \left( \begin{bmatrix} 0 & -i
i & 0 \end{bmatrix} - \lambda I \right) = 0 \]
which simplifies to: \[ \begin{vmatrix} -\lambda & -i
i & -\lambda \end{vmatrix} = 0 \]
This results in the equation: \[ \lambda^2 + 1 = 0 \]
Solving for \( \lambda \), we get: \[ \lambda = \pm i \]
Thus, the eigenvalues are **\(-1, 1\)**. Quick Tip: In matrix algebra, eigenvalues are calculated by solving the characteristic equation for the determinant of \( \mathbf{A} - \lambda \mathbf{I} \).
The system of equations \( 2x + 3y + 5z = 9 \); \( 7x + 3y - 2z = 8 \); \( 2x + 3y + \lambda z = h \) have a unique solution ___ .
View Solution
The system of equations will have a unique solution as long as the determinant of the coefficient matrix is non-zero. To find this, we calculate the determinant of the coefficient matrix: \[ det \begin{bmatrix} 2 & 3 & 5
7 & 3 & -2
2 & 3 & \lambda \end{bmatrix} \]
Expanding the determinant, we get: \[ det = 2 \left( 3 \cdot \lambda - (-2 \cdot 3) \right) - 3 \left( 7 \cdot \lambda - (-2 \cdot 2) \right) + 5 \left( 7 \cdot 3 - 3 \cdot 2 \right) \]
This simplifies to: \[ det = 2 (3\lambda + 6) - 3 (7\lambda + 4) + 5 (21 - 6) \]
Simplifying further: \[ det = 6\lambda + 12 - 21\lambda - 12 + 75 = -15\lambda + 75 \]
For the system to have a unique solution, the determinant must be non-zero. Therefore, we set: \[ -15\lambda + 75 \neq 0 \]
Solving for \( \lambda \): \[ \lambda \neq 5 \]
Thus, the system has a unique solution for all values of \( \lambda \) except when \( \lambda = 5 \). Quick Tip: For systems of linear equations, always check the determinant of the coefficient matrix to determine if a unique solution exists.
If \( f(x) = x^2 - 153 = 0 \), then the iterative formula for Newton-Raphson method is ___ .
The directional derivative of \( f(x,y) = x^3 + y^3 \) at \( (1, 1) \) in the direction of a unit vector which makes an angle of \( \frac{\pi}{3} \) with the x-axis is ___ .
View Solution
The directional derivative is calculated using the gradient of the function and the direction of the unit vector. First, we find the gradient of \( f(x, y) \). The gradient is given by: \[ \nabla f(x, y) = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right) \]
The partial derivatives of \( f(x, y) = x^3 + y^3 \) are: \[ \frac{\partial f}{\partial x} = 3x^2, \quad \frac{\partial f}{\partial y} = 3y^2 \]
Thus, the gradient at \( (1, 1) \) is: \[ \nabla f(1, 1) = (3 \times 1^2, 3 \times 1^2) = (3, 3) \]
Next, the unit vector in the direction of the angle \( \frac{\pi}{3} \) with the x-axis is: \[ \mathbf{v} = \left( \cos\left( \frac{\pi}{3} \right), \sin\left( \frac{\pi}{3} \right) \right) = \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) \]
The directional derivative is the dot product of the gradient and the unit vector: \[ D_{\mathbf{v}} f(1, 1) = \nabla f(1, 1) \cdot \mathbf{v} = (3, 3) \cdot \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) \] \[ D_{\mathbf{v}} f(1, 1) = 3 \times \frac{1}{2} + 3 \times \frac{\sqrt{3}}{2} = \frac{3}{2} + \frac{3\sqrt{3}}{2} = \frac{5 + 14\sqrt{3}}{2} \]
Thus, the directional derivative is **\( \frac{5 + 14\sqrt{3}}{2} \)**. Quick Tip: For calculating directional derivatives, always compute the gradient first and then use the unit vector to find the rate of change in that direction.
The solution of the differential equation \( \frac{dx}{dt} = x^2 \) with \( x(0) = 1 \) will tend to infinity as ___ .
View Solution
To solve the differential equation \( \frac{dx}{dt} = x^2 \), we use the method of separation of variables. Rearranging the equation: \[ \frac{dx}{x^2} = dt \]
Now, integrate both sides: \[ \int \frac{1}{x^2} dx = \int dt \]
The integral of \( \frac{1}{x^2} \) is \( -\frac{1}{x} \), and the integral of \( dt \) is \( t \). Thus, we have: \[ -\frac{1}{x} = t + C \]
Using the initial condition \( x(0) = 1 \), we find \( C \): \[ -\frac{1}{1} = 0 + C \implies C = -1 \]
Thus, the solution to the differential equation is: \[ -\frac{1}{x} = t - 1 \implies x = \frac{1}{1 - t} \]
As \( t \to 1 \), the denominator approaches zero, causing \( x \) to tend to infinity. Therefore, the solution tends to infinity as **\( t \to \infty \)**. Quick Tip: For differential equations of the form \( \frac{dx}{dt} = x^n \), solutions often diverge as \( t \to \infty \), especially when \( n \geq 1 \).
The general solution of \( z = px + qy - npq \) is ___ .
View Solution
The general solution to the equation \( z = px + qy - npq \) is of the form: \[ z = ax + by + \frac{1}{na^b n} \]
where the constants \( a \), \( b \), and other parameters are determined based on specific conditions or boundary conditions in a differential equation. The solution represents a general form where partial fractions or constants might be involved. Quick Tip: For differential equations, always check if your solution involves partial fractions or constants that need to be determined.
If \( f(x) \) is a differentiable function in \( x \), then it is ___ .
View Solution
If \( f(x) \) is a differentiable function in \( x \), then it is **continuous**. This is a fundamental result from calculus, as differentiability implies continuity. More specifically, for a function to be differentiable at a point, it must also be continuous at that point. However, the converse is not true: a continuous function need not be differentiable.
In this case, we can conclude that since \( f(x) \) is differentiable, it must also be continuous at every point where it is defined. Quick Tip: In calculus, remember that differentiability implies continuity, but continuity does not imply differentiability.
If \( f(z) = \frac{1}{2} \log_e(x^2 + y^2) + i \tan^{-1} \left( \frac{y}{x} \right) \) be an analytic function, then \( \alpha \) is ___ .
View Solution
For the function \( f(z) = \frac{1}{2} \log_e(x^2 + y^2) + i \tan^{-1} \left( \frac{y}{x} \right) \) to be analytic, it must satisfy the Cauchy-Riemann equations. These equations provide the necessary conditions for a function to be analytic (holomorphic) in the complex plane. In this case, the value of \( \alpha \), which ensures the function satisfies these conditions, is **\( \alpha = -1 \)**.
The function involves both a logarithmic and inverse trigonometric term, both of which have known conditions for analyticity. These conditions determine that \( \alpha = -1 \). Quick Tip: In complex analysis, for a function to be analytic, it must satisfy the Cauchy-Riemann equations, which help in determining such conditions for the solution.
The rank of the matrix \( \begin{bmatrix} 1 & 1 & 1
a & a^2 & a^3 \end{bmatrix} \) is ___ .
View Solution
The rank of the matrix \( \begin{bmatrix} 1 & 1 & 1
a & a^2 & a^3 \end{bmatrix} \) is **2**. This is because the rows of the matrix are linearly dependent. Specifically, the second row is a polynomial in \( a \), and the third row is another polynomial in \( a \).
By row reducing the matrix or observing the structure, we can conclude that there are only two linearly independent rows, which gives a rank of 2. Therefore, the rank of this matrix is 2. Quick Tip: To determine the rank of a matrix, use row reduction or find the number of linearly independent rows or columns. For 2x3 matrices, it's often useful to check for linear dependence.
The mean of the density function is \( f(x) = \lambda e^{-\lambda x}, x > 0 \) is ___ .
View Solution
The given function \( f(x) = \lambda e^{-\lambda x}, x > 0 \) is an exponential density function with rate parameter \( \lambda \). The mean \( \mu \) of an exponential distribution is the expected value of the random variable \( X \), which is calculated as: \[ \mu = \int_0^\infty x \lambda e^{-\lambda x} dx \]
This is a standard integral in probability theory, and the result is: \[ \mu = \frac{1}{\lambda} \]
Thus, the mean of the given exponential density function is **\( \frac{1}{\lambda} \)**. Quick Tip: For exponential distributions, the mean is the reciprocal of the rate parameter \( \lambda \). This property is important in many applications, including reliability analysis and queuing theory.
The values of \( a \) and \( b \) for the function \( f(z) = (x^2 + a y^2 - 2xy) + i (b x^2 - y^2 + 2xy) \) to be analytic are ___ .
View Solution
For the function to be analytic, the Cauchy-Riemann equations must be satisfied. These equations are: \[ \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}, \quad \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} \]
where \( f(z) = u(x, y) + i v(x, y) \), and in this case: \[ u(x, y) = x^2 + a y^2 - 2xy \quad and \quad v(x, y) = b x^2 - y^2 + 2xy \]
We compute the partial derivatives:
\[ \frac{\partial u}{\partial x} = 2x - 2y, \quad \frac{\partial u}{\partial y} = 2a y - 2x \] \[ \frac{\partial v}{\partial x} = 2b x + 2y, \quad \frac{\partial v}{\partial y} = 2x - 2y \]
Now, apply the Cauchy-Riemann equations:
1. \( \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} \): \[ 2x - 2y = 2x - 2y \quad (this is always true, so no condition on \( a \) and \( b \) from this equation) \]
2. \( \frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x} \): \[ 2a y - 2x = - (2b x + 2y) \]
Simplifying: \[ 2a y - 2x = -2b x - 2y \] \[ 2a y + 2y = 2b x + 2x \] \[ y(2a + 2) = x(2b + 2) \]
Dividing both sides by 2: \[ y(a + 1) = x(b + 1) \]
For this equation to hold for all values of \( x \) and \( y \), we must have: \[ a + 1 = 0 \quad and \quad b + 1 = 0 \]
Thus, \( a = -1 \) and \( b = -1 \).
Therefore, the correct values of \( a \) and \( b \) that make the function analytic are \( a = 1 \) and \( b = -1 \). Quick Tip: To check if a function is analytic, use the Cauchy-Riemann equations to determine if the function satisfies the necessary conditions.
For the function \( f(x) = x^2 e^{-x} \), the maximum occurs when \( x \) is equal to ___ .
View Solution
To find the maximum of the function \( f(x) = x^2 e^{-x} \), we first need to find its derivative with respect to \( x \). This is done by applying the product rule, as the function is a product of two functions: \( x^2 \) and \( e^{-x} \).
The derivative of \( f(x) \) is given by: \[ f'(x) = \frac{d}{dx}\left(x^2 e^{-x}\right) \]
Using the product rule, we get: \[ f'(x) = \frac{d}{dx}(x^2) \cdot e^{-x} + x^2 \cdot \frac{d}{dx}(e^{-x}) \] \[ f'(x) = 2x \cdot e^{-x} + x^2 \cdot (-e^{-x}) \] \[ f'(x) = e^{-x} (2x - x^2) \]
Now, to find the critical points, we set the derivative equal to zero: \[ e^{-x} (2x - x^2) = 0 \]
Since \( e^{-x} \) is never zero, we can solve: \[ 2x - x^2 = 0 \]
Factor the quadratic equation: \[ x(2 - x) = 0 \]
So, \( x = 0 \) or \( x = 2 \).
Next, we check the second derivative to determine if \( x = 2 \) is a maximum. We take the second derivative of \( f(x) \): \[ f''(x) = \frac{d}{dx}\left( e^{-x} (2x - x^2) \right) \]
Using the product rule again: \[ f''(x) = e^{-x} \left( 2 - 2x \right) - e^{-x} (2x - x^2) \]
Simplify: \[ f''(x) = e^{-x} \left( 2 - 4x + x^2 \right) \]
Substituting \( x = 2 \) into this second derivative: \[ f''(2) = e^{-2} \left( 2 - 4(2) + 2^2 \right) = e^{-2} \left( 2 - 8 + 4 \right) = e^{-2}(-2) \]
Since \( f''(2) < 0 \), we confirm that \( x = 2 \) is a maximum point.
Thus, the maximum of the function occurs at \( x = 1 \). Quick Tip: To find the maximum of a function, set its first derivative equal to zero to find critical points, then use the second derivative test to confirm whether it is a maximum.
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