Question

Find the interval in which the function x³ - 12x² + 36x + 17 is strictly increasing.

Answer 1

We have,

f(x) = x³ − 12x² + 36x + 17

⇒ f(x) = 3x² − 24x + 36 = 3(x − 6)(x − 2)

For f(x) to be increasing, we must have 

f′(x) > 0

⇒ 3(x − 6)(x− 2) > 0

⇒ x < 2 or x > 6

⇒ x ϵ (−∞, 2) ∪ (6, ∞)

So, f(x) is increasing on (−∞, 2) ∪ (6, ∞).