Determine where the function has a horizontal tangent

Question

f(x)= x-2/x^2+4

Needing help finding the answer please. Also show your work. Thanks!

Answer 1

The function has a horizontal tangent where the first derivative of the function is zero. Use the chain rule to obtain the derivative, the numerator of which is x²-4x-4. Set that numerator equal to zero and solve for x by completing the square. So 8=(x-2)². X=2+Square root of 8 or 2+2 square root of 2. Plug this value into the original function to obtain y = Square root of 2 divided by the sum of 8+4 square root of 2.