Question

Find the interval of the monotonicity of the function f(x) = 5 + 36x + 3x2 – 2x3.

Answer 1

Given f(x) = 5 + 36x + 3x2 – 2x3

⇒ f'(x) = 36 + 6x – 6x2

= – 6(x2 – x – 6)

= –6(x – 3)(x + 2)

By the sign scheme, we can say that, f(x) is strictly increases in (– 2, 3) and strictly decreases in (–∞, – 2) ∪ (3, ∞).