Question

Find the values of x for which the function f(x) = x³ – 12x² – 144x + 13

(a) increasing 

(b) decreasing.

Answer 1

f(x) = x³ – 12x² – 144x + 13

(a) f is increasing if f'(x) ≥ 0

∴ f is increasing if x ≤ -4 or x ≥ 12, 

i.e. x ∈ (-∞, -4] ∪ [12, ∞).

(b) f is decreasing if f'(x) ≤ 0

∴ f is decreasing if -4 ≤ x ≤ 12, i.e. x ∈ [-4, 12].