Match each function in List I with its behaviour at x = 0 in List II.

Match each function in List I with its…

Question 113

HardOriginal question

Match each function in List I with its behaviour at $x = 0$ in List II.

List I	List II
A. $x^{2}$	I. Neither continuous nor differentiable
B. $\lvert x \rvert$	II. Differentiable, with derivative 0
C. $\frac{\lvert x \rvert}{x}$ with value 0 at 0	III. Differentiable, though built from $\lvert x \rvert$
D. $\lvert x \rvert^{3}$	IV. Continuous but not differentiable

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

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CorrectNot quiteAnswer B

Correct answer: B

$x^{2}$ has slope 0 at 0; $\lvert x \rvert$ has a corner; $\frac{\lvert x \rvert}{x}$ jumps from $-1$ to 1.
$\lvert x \rvert^{3}$ has one-sided slopes $\pm 3x^{2} = 0$ : differentiable.

Concept: Matching functions to their behaviour
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsDifferentiability

Practise this chapter →

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

Practise this chapter →

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

Question 113

Explanation