For f(x) = 2x^3- − 3x^2 − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases.
f'(x) = 6x^2-6x-12 = 6(x^2-x-2) = 6(x+1)(x-2)
So, f' = 0 at x = -1,2
f increases on (-∞,-1) and (2,∞)
f decreases on (-1,2)
So, f' = 0 at x = -1,2
f increases on (-∞,-1) and (2,∞)
f decreases on (-1,2)