Determine the points at which the graph of the function has a horizontal tangent line. f(x) = {x^2} / {x-8}?

Answer 1

A point on a function will have a horizontal tangent line where the first derivative is zero.

Thus,

Simply the derivative to:

Set it equal to zero and solve:

x = 0 or 16 solves the equation.

Plug 0 in to f(x):

Plug 16 in to f(x):

So, the points are: (0, 0) and (16, 32)