Find the value(s) of x, so that f’(x) = 0 for the function f(x) = 4x3 – 6x2 – 24x.

Answer 1

I will assume you meant
f(x) = 4x^3 – 6x^2 – 24x

then
f'(x) = 12x^2-12x - 24
= 0
divide by 12
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 or x = -1