Second Derivative Test for Minimum

Rarely Tested

Second Derivative Test for Minimum

If:

$$f'(c)=0$$

and:

$$f''(c)>0$$

then $$f(c)$$ is a local minimum.

Usage

- Used to classify a stationary point quickly.

Question 1

Consider the function $$f:(0,\infty)\to(-\infty,\infty)$$ given by

$$f(x)=\sqrt{x}\,\log_e(x)-x+1.$$

Then which one of the following statements is TRUE?

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