According to the second derivative test, if $f'(c)=0$ and $f''(c)>0$, then $x=c$ is
Aa point of local maximum
Ba point of local minimum
Ca point where no conclusion is possible in every case
Dnecessarily a point of inflection
Answer & Solution
Correct answer: B. a point of local minimum
If $f'(c)=0$, then $c$ is a critical point. The second derivative test says $f''(c)>0$ implies the curve is concave upward there, so $x=c$ gives a local minimum. If $f''(c)<0$, it would be a local maximum.
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