Question

Find the intervals on which the function f(x) = 2x³ - 3x² - 36x+7 is

(a) strictly increasing

(b) strictly decreasing.

Answer 1

f(x) = 2x³ - 3x² - 36x+7

f’(x) = 6x² - 6x - 36

f’(x) = 6(x² - x - 6)

f’(x) = 6(x - 3)(x+2)

f’(x) is 0 at x = 3 and x = -2

F’(x)>0 for x ∈ (-∞, -2] ∪ [3, ∞)

hence in this interval function is increasing.

F’(x)<0 for x ∈ (-2 ,3)

hence in this interval function is decreasing.