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

Question

Quizplus · Accepted Answer

The critical numbers are found by setting the derivative $f'(x) = 1 - \frac{2}{x^2}$ to zero, which gives $x = \pm \sqrt{2}$. Testing these points, $-\sqrt{2}$ leads to a local maximum and $\sqrt{2}$ leads to a local minimum.

Find All Critical Numbers for the Function f(x)=x+2xf(x)=x+\frac{2}{x}f(x)=x+x2​ A) Local Maximum At

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