Match each function in List I with its left-hand and right-hand derivatives at x = 0 in List II.

Match each function in List I with its…

Question 108

MediumOriginal question

Match each function in List I with its left-hand and right-hand derivatives at $x = 0$ in List II.

List I	List II
A. $\lvert x \rvert$	I. $-2$ and $2$
B. $x + \lvert x \rvert$	II. $-3$ and $-1$
C. $\lvert x \rvert - 2x$	III. $0$ and $2$
D. $\lvert \sin 2x \rvert$	IV. $-1$ and $1$

A-I, B-III, C-II, D-IVCorrect answerYour answerA-IV, B-III, C-II, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answerA-I, B-II, C-III, D-IVCorrect answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

Write each on the two sides of 0: $\lvert x \rvert$ is $-x$ then $x$ ; $x + \lvert x \rvert$ is 0 then $2x$ ; $\lvert x \rvert - 2x$ is $-3x$ then $-x$ ; $\lvert \sin 2x \rvert$ is $-\sin 2x$ then $\sin 2x$ .
Their slopes at 0, left then right, are $-1, 1$ ; $0, 2$ ; $-3, -1$ ; $-2, 2$ .

Worth noting

$\lvert \sin 2x \rvert$ is not $\lvert x \rvert$ again: the 2 inside doubles both slopes.

Concept: One-sided derivatives
Typical timeTypical: 120 s
Your timeYours: —

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.

Question 108

Explanation