## Increasing and Decreasing Functions

### Increasing and decreasing functions

This is my third post in the series of “Applications of derivatives”. The previous two were based on “Tangent and Normal” and “Maxima and Minima”.In this post, we shall learn about increasing and decreasing functions. That is one more application of derivatives.

**Increasing and Decreasing Functions-** We shall first learn about increasing functions

**Increasing Function-**

**(a) Strictly increasing function- **A function *f *(x) is said to be a strictly increasing function on *(a, b) *if x_{1}< x2 *f(x _{1}) < f *(x

_{2}) for all x

_{l}, x

_{2}

*(a, b).*

*Thus, f(x)*is strictly increasing on

*(a, b)*if the values of f

*(x)*increase with the increase in the values of x.Refer to the graph in below-given figure