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Question

Let f(x)=2+1-x2,|x|1=2e(1-x)2,|x|>1. The points where f(x) is not differentiable are:


A

0only

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B

1,1only

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C

1 only

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D

1 only

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Solution

The correct option is B

1,1only


Explanation for the correct option:

Finding the points where f(x) is not differentiable:

Given that f(x)=2+1-x2,|x|1

f(x)=2·e(1-x)2,[x)>1.f(1+)'=limh0f(1+h))-f(1)h=limln02·eh2-2h.=limh02eh2-1h2×h.=0ea-1ex0

f(-1)=limh0(f(1+h)-f(1))h0=limh02+1-(1-h)2-f(1)h1=limh02-1-(1-h)2-2h=limh02h-h2h

f(-1)=Not defined

As f(+1)f(-1),

f(1)=does not exist

Similarly, f1(1) also does not exist

Hence f(x)is not differentiable at

x=-1and 1.

Hence, option (B) is the correct answer.


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