# Application of Derivatives for Class 12

In applications of derivatives class 12, we will study different applications of derivatives in various fields like Science, Engineering, and many other fields.

## Application of Derivatives Class 12 Concepts

The topic and subtopics covered in applications of derivatives class 12 are:

• Introduction
• Rate of Change of Quantities
• Increasing and Decreasing Functions
• Tangents and Normals
• Approximations
• Maxima and Minima
• Maximum and Minimum Values of a Function in a Closed Interval

### Application of Derivatives

Rate of change of quantity:

Consider a function y = f(x), the rate of change of a function is defined as-

$\frac{dy}{dx} = f'(x)$

Further, if two variables x and y are varying to another variable, say if x = f(t), and y = g(t), then using Chain Rule, we have:

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}},$,

where $\frac{dx}{dt} \neq 0$

Increasing and Decreasing Functions:

Consider a function f, continuous in [a,b] and differentiable on the open interval (a,b), then

(i) f is increasing in [a,b] if $f'(x)>0$ for each $x \in (a,b)$

(ii) f is decreasing in [a,b] if $f'(x)< 0$ for each $x \in (a,b)$

(iii) f is constant function in [a,b], if $f'(x) = 0$ for each $x \in (a,b)$

### Examples   