At which point does $f(x) = - x^{3} + 3 x^{2} + 9 x - 2$ have a local maximum?

-3

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-1

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1

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3

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$f'(x) = - 3 \left(x - 3\right) \left(x + 1\right)$ .
$f'$ changes from positive to negative at $x = 3$ , so $f$ rises then falls there: a local maximum.

Worth noting

At $x = -1$ the sign changes the other way: that is the local minimum.

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

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

At which point does f(x)=−x3+3x2+9x−2f(x) = - x^{3} + 3 x^{2} + 9 x - 2f(x)=−x3+3x2+9x−2 have a local maximum?