Paragraph: Let f(x)=[|x|-|x-1|]^2 Question: What is f^ (x) equal to when 0 < x < 1 ?

Correct answer: D. 8 x-4 Given f(x)=(|x|-|x+1|)^2f(x)=\ array cc 1 & x ≤ 0 (2 x-1)^2 & 0 < x < 1 1 & x ≥ 1 array . When 0 < x < 1 aligned & f(x)=(2 x-1)^2 & f^ (x)=2(2 x-1) · 2=4(2 x-1) & f^ (x)=8 x-4 aligned

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:

\text{ Let } f(x)=[|x|-|x-1|]^2

Question: What is

\mathrm{f}^{\prime}(\mathrm{x})

equal to when

0 < \mathrm{x} < 1

Options

A $0$
B $2 x-1$
C $4 x-2$
D $8 x-4$

Correct answer

D. $8 x-4$

Step-by-step solution

Given

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

\begin{array}{cc} 1 & x \leq 0 \\ (2 x-1)^2 & 0 < x < 1 \\ 1 & x \geq 1 \end{array}

\right.$ When $0 < x < 1

\begin{aligned} & f(x)=(2 x-1)^2 \\ & f^{\prime}(x)=2(2 x-1) \cdot 2=4(2 x-1) \\ & f^{\prime}(x)=8 x-4 \end{aligned}$$

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