How do you graph intervals?

A function's behavior differ and may not remain monotonous over the entire range of variable. If f(x) is a function in the variable x, then there is no reason why f(x) will be increasing monotonously or decreasing monotonously over the entire range of x. The behaviour of f(x) may be different in different sub ranges of "x". These different sub ranges of "x" in which the behavior of f(x) changes are called intervals.

Before we can plot the intervals, we need to find the intervals. We find the intervals as per following rules:

• If f'(x) is > 0, then f(x) is increasing. 
• If f'(x) = 0, f(x) is constant
• If f'(x) < 0 then f(x) is decreasing.