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Maxima & Minima · Question 20 of 80

Question 20

MediumOriginal question

Read the two statements and choose the correct option.

I. Every local maximum of a differentiable function is a critical point.

II. Every critical point of a differentiable function is a local maximum or a local minimum.

Options for question 20

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. At a local maximum of a differentiable function f′=0f' = 0, so I is true.

  2. x3x^3 has the critical point 0 that is neither, so II is false.

Concept
Critical points and extrema
Typical time
90 s
Your time
—
The rule this testsLocal extrema and the first derivative test
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Ten questions from Maxima & Minima, at your own pace.

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