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Differentiability

fx=a x2+1, x...

Question

$f (x) =$ $a x^{2} + 1, x \leq 1 = x^{2} + a x + b, x > 1$ is differentiable at x = 1, then (a, b) = _____

A

(0, 2)

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B

(2, 0)

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C

(2, 2)

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D

(0, 0)

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Solution

The correct option is A
(0, 2)

diff $\Rightarrow$ cont.

$∴$ a + 1 = 1 + a + b

b = 0

2a = a + 2

$\Rightarrow$ a = 2

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