$f'$ changes sign from negative to positive as $x$ passes through 2. What does $f$ have at $x = 2$ ?

A local maximumCorrect answerYour answerA local minimumCorrect answerYour answerA point of inflexionCorrect answerYour answerNeither a maximum nor a minimumCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Negative $f'$ before 2 means $f$ falls; positive after means it rises.
Falling then rising: a local minimum at $x = 2$ .

Worth noting

A local maximum is the other change, from positive to negative.

Concept: The first derivative test
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsLocal extrema and the first derivative test

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Ten questions from Maxima & Minima, at your own pace.

f′f'f′ changes sign from negative to positive as xxx passes through 2. What does fff have at x=2x = 2x=2?

Explanation

$f'$ changes sign from negative to positive as $x$ passes through 2. What does $f$ have at $x = 2$ ?