Which of these describes f(x) = | x - 3 | at x = 3?

Continuity & Differentiability · Question 97 of 125

Question 97

MediumOriginal question

Which of these describes $f(x) = \lvert x - 3 \rvert$ at $x = 3$ ?

Continuous but not differentiableCorrect answerYour answerContinuous and differentiableCorrect answerYour answerNeither continuous nor differentiableCorrect answerYour answerDifferentiable but not continuousCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\lvert x - 3 \rvert \to 0 = f(3)$ from both sides: continuous.
Slopes $-1$ and 1: a corner, not differentiable.

Worth noting

$\lvert x - 3 \rvert$ is $\lvert x \rvert$ moved 3 to the right, corner and all.

Concept: Testing differentiability at a point
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsDifferentiability

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Which of these describes f(x)=∣x−3∣f(x) = \lvert x - 3 \rvertf(x)=∣x−3∣ at x=3x = 3x=3?

Explanation

Which of these describes $f(x) = \lvert x - 3 \rvert$ at $x = 3$ ?