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Continuity & Differentiability · Question 118 of 125

What is f'(2) for this sum of two moduli?

Question 118

HardOriginal question

Let f(x)=∣x−1∣+∣x−3∣f(x) = \lvert x - 1 \rvert + \lvert x - 3 \rvert.

What is f′(2)f'(2) for this sum of two moduli?

Options for question 118

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. For 1<x<31 < x < 3: f(x)=(x−1)+(3−x)=2f(x) = (x - 1) + (3 - x) = 2, a constant.

  2. So f′(2)=0f'(2) = 0.

Worth noting

2 adds the slopes +1+1 and +1+1; between 1 and 3 the second modulus has slope −1-1.

Concept
A derivative on a piece of a modulus function
Typical time
150 s
Your time
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Ten questions from Continuity & Differentiability, at your own pace.

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Ten questions from Continuity & Differentiability, at your own pace.