Question

The least value of f(x) = x³ − 12x, ∈ [0, 3] is ______.

Options

• −16

• −9

• 0

• 16

Answer 1

The least value of f(x) = x³ − 12x, ∈ [0, 3] is −16.

Explanation:

Given f(x) = x³ − 12x on [0, 3].

Differentiate: f′(x) = 3x² − 12 = 0 ⇒ x = 2

Check values: f(0) = 0, f(2) = −16, f(3) = −9

Thus, the least value in the interval is −16 at x = 2.