Question

The absolute maximum value of the function f(x) = 2x³ − 3x² − 36x + 9 defined on [−3, 3] is ______.

Options

• 36

• 53

• 63

• 72

Answer 1

The absolute maximum value of the function f(x) = 2x³ − 3x² − 36x + 9 defined on [−3, 3] is 53.

Explanation:

Given f(x) = 2x³ − 3x² − 36x + 9

Now f'(x) = 6(x² − x − 6)

at f'(x) = 0

x² − x − 6

x = −2, 3

f(−2) = 2(−2)³ − 3(−2)² − 36(−2) + 9 = 53 will be absolute maximum value

f(−3) = −54 − 27 + 108 + 9 = 36

f(3) = 54 − 27 − 108 + 9 = −72