Find the intervals in which `f(x)=x^3-6x^2-36 x+2` is increasing or decreasing.

Explanation

Given as `f(x) = x^3 – 6x^2 – 36x + 2`

` f'(x) = (d/dx)(x^3 – 6x^2 – 36x + 2)`

` ⇒ f’(x) = 3x^2 – 12x – 36`

For the function `f(x)` we have to find critical point, we must have

`⇒ f’(x) = 0`

` ⇒ 3x^2 – 12x – 36 = 0`

` ⇒ 3(x^2 – 4x – 12) = 0`

`⇒ 3(x^2 – 6x + 2x – 12) = 0`
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