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Let $f (x) = \{\begin{cases} a x^{2} + 1 f o r x > 1 \\ x + a f o r x \leq 1 \end{cases}$ then $f (x)$ is derivable at $x = 1$ , if

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a=0

a=12

a=1

a=2

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detailed solution

Correct option is B

f(x)=ax2+1 for x>1x+a for x≤1 f(x)=2ax for x>11 for x≤1 2a=1⇒a=12

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Let f(x)=ax2+1 for x>1x+a for x≤1 then f(x)is derivable at x=1 , if

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Let $f (x) = \{\begin{cases} a x^{2} + 1 f o r x > 1 \\ x + a f o r x \leq 1 \end{cases}$ then $f (x)$ is derivable at $x = 1$ , if