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Derivatives & Second-Order Derivatives · Question 70 of 96

Question 70

MediumOriginal question

For f(x)=x3−6x2+9xf(x) = x^{3} - 6 x^{2} + 9 x, at what value of xx is f′′(x)=0f''(x) = 0?

Options for question 70

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. f′(x)=3x2−12x+9f'(x) = 3x^2 - 12x + 9 and f′′(x)=6x−12f''(x) = 6x - 12.

  2. 6x−12=06x - 12 = 0 gives x=2x = 2.

Worth noting

1 and 3 are where f′(x)=0f'(x) = 0, the first derivative.

Concept
Where the second derivative is zero
Typical time
90 s
Your time
—
The rule this testsSecond-order derivatives
Practise this chapter →

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Practise this chapter →

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.