Find All Critical Numbers for the Function $f(x)=x+\frac{2}{x}$ A) Local Maximum At

Multiple Choice

Find all critical numbers for the function. State whether it leads to a local maximum, a local minimum, or neither.
- $f(x) =x+\frac{2}{x}$

A) Local maximum at $-\sqrt{2}$ ; local minimum at $\sqrt{2}$
B) Local maximum at -2 ; local minimum at 2
C) Local maximum at $\sqrt{2}$ ; local minimum at $-\sqrt{2}$
D) No critical numbers; no local extrema