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]}