Test Index

NDA Math Limit, Continuity and Differentiability

Consider the function

f(x)=\left| x-1 \right|+x^2

where

x \in \mathbb{R}

[NDA I 2016]

Question : 72 of 105

Marks: +1, -0

Solution:

f(x)=|x-1|+x^{2}\;\;\;\forall\;\;\;x\in R

f_{1}(x)=|x-1|,f_{2}(x)=x^{2}

f_1(x)

and

f_2(x)

both are continuous.Hence

f(x)

is continuous

f(x)

in differentiable at

x=0

f_1(x)

is not differentiable at

x=1

Hence

f(x)

is continuous but not differentiable at

x=1

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