The function .

Differentiate the function with respect to .

The function does not have any critical numbers.

So the end points will be the maximum and minimum points.

(a)

Find the values of  at the end points of the interval .

Substitute in the function.

Substitute in the function.

Absolute maximum value is .

Absolute minimum value is .

(b)

The function and the interval is .

Find the values of  at the end points of the interval .

Since open interval is there at 4, is excluded the point.

Absolute maximum value is .

(c)

The function and the interval is .

Find the values of  at the end points of the interval .

Since open interval is there at 1, exclude that point.

Absolute minimum is .

d)

The function and the interval is .

Find the values of  at the end points of the interval .

In the interval , no absolute values are present.

No extrema.

(a) Absolute maximum value is .

Absolute minimum value is .

(b) Absolute maximum value is .

(c) Absolute minimum is .

(d) No extrema.