Functions and Derivatives

Local extrema Use the sign pattern for the derivative to identify the points where ƒ has local maximum and minimum values.

Step 1:

In this question we have to find the points where ƒ has local maximum and minimum values given that the derivative is .

Step 2:

From the above equation ƒ has local maximum or minimum values when . i.e. when

. When approaches from the left side of say (),

Therefore, has local minimum at .

Step 3:

When approaches from the left side of say (),

Therefore, has local maximum at .