Question

Locate the absolute extreama of the function on the closed interval.

f (x) = x^3 - 3/2 x^2,       [-1, 2]

Answer 1

Step 1 :

The function is and the interval .

Differentiate with respect to x.

Find the critical numbers of on by setting .

The critical points are and .

Step 2 :

Find the values of at these critical numbers.

Step 3 :

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

Compare the four values of to find absolute maximum and absolute minimum.

Absolute maximum value is

Absolute minimum value is

Solution:

Absolute maximum value is

Absolute minimum value is