NCERT Solutions For Class 12 Mathematics Chapter 6 Application of Derivatives

Education Journalist | Study Abroad Strategy Lead

NCERT Solutions for Class 12 Mathematics Chapter 6 Application of Derivatives covers important concepts of determinants, rate of change of quantities, tangents and normals, increasing and decreasing functions, Approximations, Maxima and minima and many more. The word “Derivative” comes from “derive” meaning to get or obtain something from something else. A derivative is an expression that provides us with the rate of change of a function related to an independent variable.

The chapter Calculus with chapters Continuity and Differentiability and Application of Derivatives Class 12 has a weightage of 10 marks in the CBSE Class 12 examination. Questions related to increasing or decreasing functions, tangents and normals, maxima and minima are generally asked in the examination. Simple problems demonstrating basic principles and understanding of derivatives are also included.

Download PDF: NCERT Solutions for Class 12 Mathematics Chapter 6

NCERT Solutions for Class 12 Mathematics Chapter 6 Application of Derivatives

Important Topics in Class 12 Mathematics Chapter 6 Application of Derivatives

Rate of change of quantity – If we have a function y = f(x), then the rate of the change of function is defined as dy/dx = f'(x).

Further, if the two variables x and y are varying to some other variable, say if x = f(t), and y = g(t), then using the Chain Rule, we have: dy/dx = (dy/dt)/(dx/dt) where dx/dt isn’t equal to 0.

Increasing and Decreasing Functions – Consider a function f that is continuous in [a,b] and differentiable on the open interval (a,b), then the function can be determined to be increasing or decreasing in the following way.

f is increasing in [a,b] if f'(x) > 0 for each x in (a,b) f is decreasing in [a,b] if f'(x) < 0 for each x in (a,b) f is a constant function in [a,b], if f'(x) = 0 for each x in (a,b)

Finding tangents and normals for a given curve is necessary to find the maxima and minima of the function, in turn.

A tangent at a point on a curve is a straight line that touches the curve at that specific. Its slope is equal to the gradient or derivative of the curve at that point. A normal is a straight line at a point on the curve that intersects the curve at that particular point and is perpendicular to the tangent at that point.

NCERT Solutions For Class 12 Maths Chapter 6 Exercises

The detailed solutions for all the NCERT Solutions for Chapter 6 Application of Derivatives under different exercises are as follows:

Also Read:

Related Articles
Approximations	Derivatives	Interpolation Formula
Lagrange Interpolation Formula	Linear Approximation Formula	Linear Interpolation Formula
Linear Regression Formula	Newton Method Formula	Differential Calculus Approximation

Check-Out:

PCMB Study Guides
NCERT Solutions for Class 12 Physics	Class 12 Physics Notes	Formulas in Physics
Topics for Comparison in Physics	Choice-based questions in physics	Topics in relation to physics
Physics Study Notes	Class 12 Physics Book PDF	Class 12 Physics Practicals
Important Derivations in Physics	SI units in Physics	Important Physics Constants and Units
Class 12 Physics Syllabus	Mendeleev's Periodic Table	NCERT Solutions for Class 12 Biology
NCERT Solutions for Class 12 English	NCERT Solutions for Class 11 Chemistry	Class 12 Chemistry Practicals
Class 12 Chemistry Notes	Important Chemical Reactions	Class 12 Maths Notes
Class 12 PCMB Notes	NCERT Class 12 Biology Book	NCERT Class 12 Maths Book
NCERT Class 12 Textbooks	NCERT Solutions for Class 11 Maths	NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 12 Maths	NCERT Solutions for Class 11 Biology	NCERT Solutions for Class 11 English
NCERT Class 11 Chemistry Book	NCERT Class 11 Physics Book	NCERT Class 11 Biology Book
Class 11 Notes	Important Maths Formulas	Important Chemistry Formulas
Class 11 PCMB Syllabus	Chemistry Study Notes	Biology Study Notes
Periodic Table in Chemistry	Important Chemical Reactions	Comparison topics in Chemistry
Comparison Topics in Maths	Biology MCQs	Important Named Reactions
Maths MCQs	Comparison Topics in Biology	Chemistry MCQs

CBSE CLASS XII Related Questions

1.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

View Solution

2.
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions:

(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
(iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female.
OR
(iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male.

View Solution

3.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]

View Solution

4.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.

View Solution

5.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

View Solution

6.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).

View Solution

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

NCERT Solutions for Class 12 Mathematics Chapter 6 Application of Derivatives

Important Topics in Class 12 Mathematics Chapter 6 Application of Derivatives

NCERT Solutions For Class 12 Maths Chapter 6 Exercises

CBSE CLASS XII Related Questions

1.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

5.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

Similar Mathematics Concepts

Comments

dOGVmW

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

NCERT Solutions for Class 12 Mathematics Chapter 6 Application of Derivatives

Important Topics in Class 12 Mathematics Chapter 6 Application of Derivatives

NCERT Solutions For Class 12 Maths Chapter 6 Exercises

CBSE CLASS XII Related Questions

1.Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

5.Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

Similar Mathematics Concepts

Comments

dOGVmW

1.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

5.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).