Question

Find the intervals on which each of the following functions is (a) increasing (b) decreasing.

f(x) = (6+12x+3x² - 2x³)

Answer 1

f(x) = -2x³+3x²+12x+6

f’(x) = -6x²+6x+12

f’(x) = -6(x² - x - 2)

= -6(x - 2)(x+1)

Function f(x) is increasing for x ∈ [-1,2] and decreasing in x ∈ (-∞,-1) ∪ (2, ∞)