increasing and decreasing functions

Let us learn about increasing and decreasing functions

A function is called increasing when it increases as the variable increases & decreases as the variable decreases. A function is called decreasing when it decreases as the variable increases & increases as the variable decreases.

The graph of a function specifies plainly whether it is increasing or decreasing.

The derivative of a function can be used to determine whether the function is decreasing or increasing on any intervals in its domain. Incase f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) <>decreasing on I. Because the derivative is 0 or does not exist only at critical points of the function, it must be negative or positive at all other points where the function exists.

Theorem on Decreasing or Increasing of Functions:

Let letter “f” be continuous on [a, b] & differentiable on the open interval (a, b).

(a) “f” is decreasing on [a, b] if f '(x) <> ε(a, b)

(b) “f” is increasing on [a, b] if f '(x) > 0 for each x ε(a, b)

Theorem on Decreasing or Increasing of Functions can be proved by using Mean Value Theorem.

Theorem on Decreasing or Increasing of Functions can be used in various problems to check whether a function is increasing or decreasing.

In our next blog we shall learn about structure of nephron I hope the above explanation was useful.Keep reading and leave your comments.