Find the critical points. Then find and classify all the extreme values. $$f(x)=\sqrt{x}-\frac{1}{\sqrt{x}}$$
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These are the points where the derivative is either zero or undefined. To find the derivative of $f(x)$, we can use the power rule and the chain rule: $$f'(x) = \frac{1}{2\sqrt{x}} + \frac{1}{2x\sqrt{x}} = \frac{\sqrt{x}+1}{2x\sqrt{x}}$$ Now we can set $f'(x) Show more…
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