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UPSC NDA I 2016 Mathematics Solved Paper

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For the next five items that follow :
Consider the function
f(x)=|x−1|+x2
where x∊ℝ

[NDA I 2016]

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Question : 18

Total: 120

Which one of the following statements is correct ?

f(x) is continuous but not differentiable at x=0
f(x) is continuous but not differentiable at x=1
f(x) is differentiable at x=1
f(x) is not differentiable at x=0 and x=1

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