Step 1:

a)

The function and the interval is .

Differentiate the function with respect to

Find the critical numbers of on by setting .

Critical number is 

Step 2:

Find the values of at this critical number .

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

Compare the three values of to find absolute extrema of the function.

Absolute maximum value is

Absolute minimum value is

step 3:

b)

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 maximum value is

Step 4:

c)

The function and the interval is .

Find the value of the function at critical number .

Since open interval is there at 2, exclude that point.

Absolute minimum value is .

Step 5:

d)

The function and the interval is .

Find the value of the function at critical number .

Since open interval is there at 4, exclude that point.

Absolute minimum value is .

Solution:

a)

Absolute maximum value is

Absolute minimum value is

b)

Absolute maximum value is

c)

Absolute minimum value is .

d)

Absolute minimum value is .