(a)

The function is , .

Graph :

Graph the function  :

Observe the graph.

The absolute maximum at  is .

The absolute minimum at  is .

(b)

Absolute values of a function exist either at the end points or at the critical points. 

Evaluate the critical points.

The function is .

Differentiate  on each side with respect to .

To find the critical points equate  to zero.

 and 

 and 

 and .

Find the maximum and minimum values.

Substitute the critical points in the function.

Substitute  in .

Substitute  in .

Evaluate the function at the end points.

The function is .

Substitute  in .

Substitute  in .

The maximum value of the function is at .

The minimum value of the function is at .

The absolute maximum is .

The absolute minimum is .

The absolute maximum is .

The absolute minimum is .