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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2017 · Mathematics · Continuity and Differentiability

If f(x)=x( x - x+1 ) , then f(x) is

If f(x)=x(x−x+1)f(x)=x(\sqrt{x}-\sqrt{x+1}), then f(x)f(x) is

Options

  1. Acontinuous but not differentiable at x=0x=0
  2. Bdifferentiable at x=0x=0
  3. Cnot continuous at x=0x=0
  4. DNone of the above

Correct answer

B. differentiable at x=0x=0

Step-by-step solution

f(x)=x(x−x+1)f(x)=x(x−x+1)(x+x+1)(xx+1)\begin{aligned} & f(x)=x(\sqrt{x}-\sqrt{x+1}) \\ & f(x)=\frac{x(\sqrt{x}-\sqrt{x+1})(\sqrt{x}+\sqrt{x+1})}{(\sqrt{x} \sqrt{x+1})}\end{aligned}=\frac{x(x-x-1)}{\sqrt{x}+\sqrt{x+1}}=\frac{-x}{\sqrt{x}+\sqrt{x+1}}Hence,Hence,\mathrm{f}(\mathrm{x})iscontinuousaswellasdifferentiableatis continuous as well as differentiable at\mathrm{x}=0$.
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