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Question

Test the continuity and differentiability of the function defined as under at x=1 and x=2.f(x)=x,x<12x,1x22+3xx2x>2

A
Continuous and differentiable at both points
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B
Dis-Continuous and not -differentiable at both points
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C
Continuous at both points but differentiable at x=2 only
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D
Continuous at both points but differentiable at x=1 only
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Solution

The correct option is C Continuous at both points but differentiable at x=2 only
f(x)=x,x<12x,1x22+3xx2x>2
f(1)=1 and f(1+)=1
f is continuous at x=1
f(2)=0 and f(2+)=0
f is continuous at x=2
f(x)=1,x<111x232xx>2
f(1)=1 and f(1+)=1
f is not differential at x=1
f(2)=1 and f(2+)=1
f is differential at x=2

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