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

Continuity & Differentiability · Question 112 of 125

Question 112

HardOriginal question

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

a = \frac{1}{2},\ b = \frac{1}{2}

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a = 1,\ b = 1

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a = \frac{1}{2},\ b = \frac{3}{2}

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a = 2,\ b = 2

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CorrectNot quiteAnswer A

Correct answer: A

Worth noting

$a = 1,\ b = 1$ joins the values but leaves slopes 2 and 1.

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

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