Extreme Values

Does have an absolute minimum value? An absolute maximum? If so, find them or give reasons why they fail to exist. List all critical points of ƒ.

Step 1 of 3 :

In this problem, we have to find an absolute minimum of absolute maximum the list the critical points of function.

Step 2 of 3 :

Given function is

is continuous and defined for all real x .

Solve for x by equating to zero

Let us find the end behaviour of the function

Conclude that has no absolute minimum and that if it has a maximum it is achieved in [-7,11/3].

Since is continuous, we are guaranteed that the absolute maximum is indeed achieved in that interval.