Question

Find all points on the graph of f(x)=-x^3 + 3x^2 - 2 at which there is a horizontal tangent line.

Answer 1

I feel bad to have skipped this one earlier. Anyway, you must first find the first derivative.

f'(x) = -3x^2 + 6x

Then you must find the points at which f'(x) = 0.

f'(x) = 3x(3-x)
0 = 3x; x = 0
0 = 3-x; x = 3

x = 0 and 3

Answer 2

Okay, but where did you get 3x(3-x)? And is it okay if I ask you another question in this question? I'm not sure if that's allowed or not, I just started using this site haha.

Answer 3

I factored out a 3x from the derivative