Question

f(x) = 2x³ – 9x² + 12x + 5.

Answer 1

f(x) = 2x³ – 9x² + 12x + 15

f'(x) = 6x² – 18x + 12

= 6(x² – 3x + 2)

x = 1 and x = 2 divides the real number line into three intervals (-∞, -1), (1, 2) and (2,∞).

when x ∈ (-∞, 1) then f'(x) = + ve

when x ∈ (1,2) then f'(x) = – ve

when x ∈ (2,∞) then f'(x) = + ve

So, function is increasing in interval (-∞, 1) ∪ (2,∞) and decreasing in interval (4, 2).