# How do you find the points where the tangent line is horizontal given #y=16x^-1-x^2#?

##### 1 Answer

The point at which the tangent line is horizontal is

To find the points at which the tangent line is horizontal, we have to find where the slope of the function is 0 because a horizontal line's slope is 0.

That's your derivative. Now set it equal to 0 and solve for x to find the x values at which the tangent line is horizontal to given function.

We now know that the tangent line is horizontal when

Now plug in

The point at which the tangent line is horizontal is

You can confirm this by graphing the function and checking if the tangent line at the point would be horizontal:

graph{(16x^(-1)) - (x^2) [-32.13, 23, -21.36, 6.24]}