What are the local extrema, if any, of f(x)= 4x+6/x ?

Differentiating we have $f ' \left(x\right) = 4 - \frac{6}{x} ^ 2$. We set this equal to 0, as a necessary condition. This gives $4 - \frac{6}{x} ^ 2 = 0$ so we have $\sqrt{\frac{3}{2}}$ and $- \sqrt{\frac{3}{2}}$ as our extrema.