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

NDA 2016 · Mathematics · Continuity and Differentiability

Paragraph: Let f(x)=[|x|-|x-1|]^2 Question: What is f^ (x) equal to...

Paragraph:  Let f(x)=[∣x∣−∣x−1∣]2\text{ Let } f(x)=[|x|-|x-1|]^2Question: What is f′(x)\mathrm{f}^{\prime}(\mathrm{x}) equal to when x>1\mathrm{x} > 1 ?

Options

  1. A00
  2. B2x−12 x-1
  3. C4x−24 x-2
  4. D8x−48 x-4

Correct answer

A. 00

Step-by-step solution

Given f(x)=(|x|-|x+1|)^2f(x)=\left\{1x≤0(2x−1)20<x<11x≥1\begin{array}{cc} 1 & x \leq 0 \\ (2 x-1)^2 & 0 < x < 1 \\ 1 & x \geq 1 \end{array}\right. When x>1f(x)=1f′(x)=0\begin{aligned} & \text{ When } x > 1 \\ & f(x)=1 \\ & f^{\prime}(x)=0\end{aligned}$$
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