# How to tell if a function is increasing or decreasing from derivative?

Increasing functions are those functions that increase monotonically within a particular domain, and decreasing functions are those which decrease monotonically within a particular domain. We check for the monotonicity of a function using derivatives within the given domain. Let's find out how.

## Answer: If the first derivative of a function is greater than zero in a particular interval, then it is said to be increasing in that interval, and vice-versa for decreasing function.

Let's understand the statement in detail.

**Explanation:**

Let's take an example of a function f(x) = x^{3} + x^{2} + 3x + 2. Let's find its monotonicity in the domain of real positive numbers.

First of all, we find its first derivative.

Hence, f'(x) = 3x^{2} + 2x + 3.

Now since the function f'(x) is always positive for all the positive real numbers, it is said to be increasing in the domain of real positive numbers.