Question

Find the interval of the monotonicity of the function f(x) = 2x³ – 12x² + 18x + 5.

Answer 1

Given f(x) = 2x³ – 12x² + 18x + 5

= 6x² – 24x + 18

= 6(x² – 4x + 3)

= 6(x² – 4x + 3)

= 6(x – 1)(x – 3)

By the sign scheme, f(x) is strictly increases in (–∞, 1) ∪ (3, ∞) and strictly decreases in (1, 3)