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Question

If f(x)=ax2b,if|x|<11|x|if|x|1 is differential at x=1. Find the values of a and b

A
a=1/2; b=3/2
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B
a=1/2; b=3/2
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C
a=1/2; b=3/2
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D
a=1/2; b=3/2
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Solution

The correct option is A a=1/2; b=3/2
f(x)=⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ax2b;1<x<11x;x11x;x1
Now f(x) is differentiable at x=1
2ax=1x2 at x=1
a=12
Also f(x) is continuous at x=1
a(1)2b=1
b=32

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