horizontal tangent line of f (x) = -x^3+3x^2-2?

Question

find the points of

Answer 1

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when tangent is horrizontal, f'(x) = 0

i.e. f'(x) = -3x^2 + 6x = 0

or x(x-2) =0

x = 0,2

So tangent is horrizontal at x=0 or 2 so put back in

f(0) = -2, f(2) = 2

Thus the required points are (0,-2) and (2,2)