Question

At what values of x does the function f(x)= x(x-4)^4 have a horizontal tangent line?

Answer 1

Tagent is horizontal when f'(x)=0.

However, f'(x) is a polynomial of degree 4, but have 3 coincident roots, so you will have only 2 distinct roots. f'(x) has rational factors, so it would not be too difficult to figure out the roots.
Here's an image to help you.
http://img21.imageshack.us/img21/5355/1291286326.png