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Question

Let f(x)={x2,ifxx0ax+b,ifx>x0lf f is differentiable at x0 then

A
a=x0,b=x0
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B
a=2x0,b=x20
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C
a=2x0,b=x20
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D
a=x0, b=x20
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Solution

The correct option is A a=2x0,b=x20
f(x)={x2,ifxx0ax+b,ifx>x0
Since, f is differentiable
Therefore, f and f are continuous function
For continuity of f
LHL=RHL
x02=ax0+b ....(1)
Now, f(x)={2x,ifxx0a,ifx>x0
For continuity of f
LHL=RHL
2x0=a .....(2)
From (1) & (2)
b=(x0)2

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