# 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