# Thread: Finding minima/maxima/point of inflection

1. ## Finding minima/maxima/point of inflection

For f(x) = (2x^2)+(8/x^2) when finding where y = 0 in the first derivative function, it doesn't exist?

The 1st derivative is f'(x) = 4x - 16^-3
and then I make it 0 = 4x - 16^-3
But there is no solution to that.
So what is it classified as because my question is asking me to find maximum/minimum and any points of inflexion
The 2nd derivative is f''(x) = 4 + 48^-4
But I can't go further because there is no solution to x?

2. There are three roots to your derivative. $0=x(4-16x^2)$ now we know that $4-16x^2=(2-4x)(2+4x)$ so you have three solutions. these would be the turning points. I assume you can do the rest