For which a and b is f(x) = ax + b if x < 2; x^2 - 1 if x ≥ 2 differentiable at x = 2?

Continuity & Differentiability · Question 120 of 125

Question 120

HardOriginal question

For which $a$ and $b$ is $f(x) = \begin{cases} ax + b, & x < 2 \\ x^{2} - 1, & x \ge 2 \end{cases}$ differentiable at $x = 2$ ?

a = 4,\ b = -5

Correct answerYour answer

a = 4,\ b = 3

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a = 2,\ b = -1

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a = -5,\ b = 4

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Worth noting

$a = 2,\ b = -1$ joins the values but takes the slope as 2 instead of $2x = 4$ .

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

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