If f has a local minimum at x = 2, then what can you say about $f ^ { \prime } ( 2 )$ ? What if you also know that f is differentiable at x = 2?

Name: If f has a local minimum at x = 2, then what can you say about $f ^ { \prime } ( 2 )$ ? What if you also know that f is differentiable at x = 2?
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Question

Quizplus · Accepted Answer

The Answer is Either

f ^ { \prime } ( 2 ) = 0 ext { or } f ^ { \prime } ( 2 )

is undefined. If we also know that f is differentiable at x = 2, then

f ^ { \prime } ( 2 ) = 0

If F Has a Local Minimum at X = 2 f′(2)f ^ { \prime } ( 2 )f′(2)

If F Has a Local Minimum at X = 2 $f ^ { \prime } ( 2 )$