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Single Variable Calculus

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Critical Points, Inflection Points and Derivatives

SVCALC-WYIXZ8

Which of the following situations is impossible for a function $f$?

A

$f''(c)=0$ but $c$ is not an inflection point

B

Every point in $f$'s domain is a critical point

C

$c$ is a local maximum but $f'(c)\not=0$

D

$c$ is an inflection point but $f''(c)\not=0$

E

$f(c)$ undefined but $c$ is a local extremum