NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

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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:

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CBSE CLASS XII Related Questions

1.
Find the vector and cartesian equations of the line passing through the point of intersection of the lines $ \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) $ and $ \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) $ and parallel to the line $ \frac{x - 1}{-2} = \frac{7 - y}{-3} = z $.
View Solution
2.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of $p$ and $q$.
- $p = -\frac{2}{3}, \, q = \frac{5}{3}$
- $p = -\frac{8}{3}, \, q = \frac{20}{3}$
- $p = \frac{20}{3}, \, q = -\frac{8}{3}$
- $p = 0, \, q = 0$
View Solution
3.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is
- Reflexive only
- Reflexive and Transitive
- Symmetric and Transitive
- Symmetric only
View Solution
4.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
5.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.
6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]
View Solution