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Derivatives & Second-Order Derivatives · Question 72 of 96

Question 72

MediumOriginal question

For f(x)=log⁡(x+1)f(x) = \log{\left(x + 1 \right)}, what is f′′(1)f''(1)?

Options for question 72

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. f′(x)=1x+1f'(x) = \frac{1}{x + 1} and f′′(x)=−1(x+1)2f''(x) = - \frac{1}{\left(x + 1\right)^{2}}.

  2. So f′′(1)=−14f''(1) = - \frac{1}{4}.

Worth noting

12\frac{1}{2} is f′(1)f'(1), one derivative short.

Concept
Second derivative at a point
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.