Which of these describes f(x) = | x + 2 | at x = 0?

Continuity & Differentiability · Question 90 of 125

Question 90

EasyOriginal question

Which of these describes $f(x) = \lvert x + 2 \rvert$ at $x = 0$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Near 0, $x + 2 > 0$ , so $f(x) = x + 2$ .
A linear function there: continuous and differentiable, with $f'(0) = 1$ .

Worth noting

The corner of $\lvert x + 2 \rvert$ is at $x = -2$ , where the inside is 0, not at the origin.

Concept: Testing differentiability at a point
Typical timeTypical: 60 s
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Which of these describes f(x)=∣x+2∣f(x) = \lvert x + 2 \rvertf(x)=∣x+2∣ at x=0x = 0x=0?

Explanation

Which of these describes $f(x) = \lvert x + 2 \rvert$ at $x = 0$ ?