Question

The maximum and minimum values for the function f(x) = 4x³ - 6x² on [-1, 2] are ______

Options

• 2, 0

• 0, -2

• 16, -2

• -2, 16

Answer 1

The maximum and minimum values for the function f(x) = 4x³ - 6x² on [-1, 2] are 0, -2.

Explanation:

f(x) = 4x³ - 6x²

∴ f'(x) = 12x² - 12x

∴ x²(x - 1) = 0 ⇒ x = 1, 0

Now f''(x) = 24x - 12

f''(1) = 12 > 0

f''(0) = -12 < 0

f(1) = 4 - 6 = -2

f(0) = 0

∴ Maximum at 0 and Minimum at 1 and

Maximum value is 0 and Minimum value is -2.