Question

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

Answer 1

The tangent line equation is
y=f'(x)(x-x0)+f(x0) but i don understand the question.

Answer 2

f'(x)=-3x^2+6x, that's all I got. You suppose to find all the points.
A. (0, -2), (2, 2)
B. (0, -2)
C. (1, 0), (0, -2)
D. (2, 2)
E. None of these

Answer 3

Horizontal tangents occur where the derivative / slope of the function is 0.
We simply need to take the derivative of our function to find the equation of slope at any point. Set the derivative equal to 0 and solve for x for the points where the slope is horizontal / 0.

Answer 4

I got it. Thanks.