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If the function f (x)= {{:(e ^(2x) -1","...

If the function `f (x)= {{:(e ^(2x) -1",","when " x le 0),(ax+ (bx^(2))/(2)",","when " xgt0):}` is differentiable at `x=0` then-

A

`a=1, b =2`

B

`a =2, b=` any value

C

`a =2, b=4`

D

`a=` any value, `b=4`

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The correct Answer is:
B
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