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Continuity & Differentiability · Question 101 of 125

At how many points is this sum of two moduli not differentiable?

Question 101

MediumOriginal question

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

At how many points is this sum of two moduli not differentiable?

Options for question 101

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Corners at x=1x = 1 and x=3x = 3, where each inside is 0.

  2. 2 points.

Worth noting

1 counts only the midpoint, where nothing special happens.

Concept
Counting points where a function is not differentiable
Typical time
120 s
Your time
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The rule this testsDifferentiability
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Ten questions from Continuity & Differentiability, at your own pace.

Practise this chapter →

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