Question

Find the interval in which the following function is strictly increasing or strictly decreasing f(x) = 20 – 9x + 6x2 – x3.

Answer 1

f'(x) = 0 ⇒ – 9 + 12x – 3x2 = 0

⇒ – 3(x2 – 4x + 9) = 0

⇒ –(3) (x – 1) (x – 3) = 0

⇒ x = 1, x = 3

∴ The intervals are (–∞, 1), (1, 3), (3, ∞)

So, f(x) is strictly decreasing in

(–∞, 1) ∪ (3, ∞) and strictly increasing in (1, 3).