Question

 Find the absolute maximum and absolute minimum values of  on the given interval.

f (x) = 2x3 - 3x2 - 12x + 1,    [-2, 3]

Answer 1

Step 1:

The function and the interval is .

Differentiate the function with respect to

Find the critical numbers of on the interval by setting .

and .

Critical numbers 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