Find the intervals in which the function f given by `f(x)=2x^3-3x^2-36 x+7`is (a) strictly increasing (b) strictly decreasing

Explanation

`f(x) = 2x^(3) - 3x^(2)-36x+7`
` rArr f'(x) = 6x^(2) - 6x - 36`
` = 6(x^(2)-x-6) = 6 (x-3)(x+2)`
Let f'(x) =0
` rArr 6(x-3)(x+2)=0`
` rArr x=3 or x=-2`

(a) f(x) is strictly increasing in ` (-infty, -2) cup (3, infty)`.
(b) f(x) is strictly decreasing in ` (-2, 3)`.