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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2016 · Mathematics · Continuity and Differentiability

Consider the function f(x)=|x-1|+x^2 , where x ∈ R . Which one of...

Consider the function f(x)=∣x−1∣+x2\mathrm{f}(\mathrm{x})=|\mathrm{x}-1|+\mathrm{x}^2, where x∈R\mathrm{x} \in \mathrm{R}. Which one of the following statements is correct?

Options

  1. Af(x)\mathrm{f}(\mathrm{x}) is continuous but not differentiable at x=0\mathrm{x}=0
  2. Bf(x)f(x) is continuous but not differentiable at x=1x=1
  3. Cf(x)\mathrm{f}(\mathrm{x}) is differentiable at x=1\mathrm{x}=1
  4. Df(x)\mathrm{f}(\mathrm{x}) is not differentiable at x=0\mathrm{x}=0 and x=1\mathrm{x}=1

Correct answer

B. f(x)f(x) is continuous but not differentiable at x=1x=1

Step-by-step solution

f(x)=∣x−1∣+x2∀x∈Rf1(x)=∣x−1∣,f2(x)=x2\begin{aligned} & f(x)=|x-1|+x^2 \quad \forall \quad x \in \mathbb{R} \\ & f_1(x)=|x-1|, f_2(x)=x^2 \end{aligned}f_1(x)andf2(x)botharecontinuous.Henceand f_2(x) both are continuous. Hencef(x)iscontinuous.is continuous.f(x)indifferentiableatin differentiable atx=0f_1(x)isnotdifferentiableatis not differentiable atx=1.Hence. Hencef(x)iscontinuousbutnotdifferentiableatis continuous but not differentiable atx=1$.
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