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Question

lf f(x)=11x2, then f(x) is

A
Continuous on [1,1] and differentiable on (1,1)
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B
Continuous on [1,1] and differentiable on (1,0)(0,1)
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C
Continuous and differentiable on [1,1]
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D
Continuous and differentiable on (1,1)
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Solution

The correct option is A Continuous on [1,1] and differentiable on (1,1)
f(x)=11x2forx(1,1)letx=sin(t)fort(π2,π2)f(t)=1cos(t)=2sin(t/2)Theabovefunctioniscontinuousaswellasdifferentiableforx(1,1)
Hence, the answer is "A"

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