Determine the point at which the graph of the function below has a horizontal tangent line. (If the function has no horizontal tangent line, enter NONE.) y = x3 + 9x

Question

I understand the basic idea that it needs to be equal to zero and of course is horizontal, but this specific problem is a bit transfixing. It only gives the option to enter one coordinate or to enter NONE. Thank you for the help!

Answer 1

The derivative is 3x^2 + 9, which is greater than or equal to 9. Thus, the derivative never equals 0 but exists everywhere, so there is no horizontal tangent.