Question

How do you find the points where the graph of the function `f(x) = x^4 - 4x^3` has horizontal tangents?

Answer 1

That will happen when the derivate is zero. In x=0 and x=3.

Explanation:

`(x^4-4x^3)'=4x^3-12x^2`

`4x^3-12x^2=4x^2(x-3)`, which as zeros in x=0 and x=3.