Learn Class 12 Math - Application of Derivatives

The term application of derivatives refers to the term rate of changing in the quantities, increasing and decreasing functions, maxima and minima, and many other terms. The maxima and minima of the functions include the maximum and minimum values of the function that are present in the functions.

Rate of change of quantity

• The term rate of quantity includes the rate of change of functions.
• Mainly the derivatives are denoted by the dy or dx functions.
• f'(x) = dy/dx
• Whereas dy/dx = dy/dt * dx/dt

Increasing & Decreasing functions

We have to assume that the f is a function differential in (a,b) where as closed in [a,b].

• The term rate of quantity includes the rate of change of functions.
• Mainly the derivatives are denoted by the dy or dx functions.
• If f'x is greater than zero, then it is always an increasing function.
• If f'x is lesser than zero, then it is always considered as the decreasing function.
• If f'x is equal to zero, then it is considered as the constant function.

Maxima & Minima

• Maxima and Minima are the main functions.
• It is considered as the maximum and minimum value of the functions for the different sets of ranges.
• The maximum value is known as maxima.
• The minimum value is known as minima.
• The point of Maxima lies at the top whereas the minimum point will lie at the bottom.