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Question

If f(x)={aeax,x0x34x+2b,x>0

is differentiable at x=0, then the value of |a|+b21 is


Your Answer
A
3
Correct Answer
B
2
Your Answer
C
0
Your Answer
D
None of the above

Solution

The correct option is C 2
At x=0
L.H.D. =a2eaxx=0=a2
R.H.D =3x24x=0=4
L.H.D. = R.H.D.
a2=4  a2=4|a|=2 

Function is differentiable at x=0
Function is continuous at x=0
L.H.L. =limx0 aeax 
R.H.L. =limx0+ x34x+2b
L.H.L. = R.H.L.
 a=2b
a2=4b2
b2=a24=44=1 
|a|+b21=2+11=2

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