Which of these describes f(x) = | x^2 - 9 | at x = 3?

Continuity & Differentiability · Question 102 of 125

Question 102

MediumOriginal question

Which of these describes $f(x) = \lvert x^{2} - 9 \rvert$ at $x = 3$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Both sides tend to 0 = $f(3)$ : continuous.
Slopes $-2x = -6$ and $2x = 6$ : a corner.

Worth noting

The modulus folds the curve up where $x^{2} - 9$ changes sign, leaving a corner.

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)=∣x2−9∣f(x) = \lvert x^{2} - 9 \rvertf(x)=∣x2−9∣ at x=3x = 3x=3?

Explanation

Which of these describes $f(x) = \lvert x^{2} - 9 \rvert$ at $x = 3$ ?