\

(a)

\

The function is $\"\"$ .

\

Graph :

\

Graph the function $\"\"$ :

\

$\"\"$

\

Observe the graph.

\

The absolute maximum at $\"\"$ is $\"\"$ .

\

The absolute minimum at $\"\"$ and $\"\"$ 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 $\"\"$ .

\

The end points of the function are $\"\"$ and $\"\"$ .

\

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 $\"\"$ .