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Continuity & Differentiability · Question 114 of 125

Question 114

HardOriginal question

At how many points is f(x)=∣x−1∣+∣x−2∣+∣x−3∣f(x) = \lvert x - 1 \rvert + \lvert x - 2 \rvert + \lvert x - 3 \rvert not differentiable?

Options for question 114

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. The corners are at 1, 2 and 3.

  2. At each, the slope jumps by 2, so all 3 are points of non-differentiability.

Worth noting

1 guesses that the middle corner is the only one; each modulus brings its own.

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.

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

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