Question

How Do You Check If A Function Is Monotonically Increasing?

Answer 1

Explanation of conditions to check if a function is monotonically increasing:

A monotonic function is a function which is either entirely increasing or decreasing .

A monotonically increasing function is always increasing in its domain ,

To determine if a function is monotonically increasing

1: Calculate first derivative of the function $(f\text{'}x)$

2: Check if the derivative of a function is always positive or negative, if positive then the function is monotonically increasing

For example:

$y=3x+2$

$f\text{'}\left(x\right)=3$which is always positive.

So, function $y=3x+2$is monotonically increasing.

Hence, if function's derivative is positive in its domain, then the function is monotonically increasing .