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