Q228 / 270 · NDA 2016 (Phase 2) · Mathematics
Paragraph:
$\text { Let } f(x)=[|x|-|x-1|]^2$
Question:
What is $\mathrm{f}^{\prime}(\mathrm{x})$ equal to when $\mathrm{x} \gt 1$ ?
Question: What is $\mathrm{f}^{\prime}(\mathrm{x})$ equal to when $\mathrm{x} \gt 1$ ?
- Correct answerA$0$
- B$2 x-1$
- C$4 x-2$
- D$8 x-4$
Solution
Given $f(x)=(|x|-|x+1|)^2$
$f(x)=\left\{\begin{array}{cc}
1 & x \leq 0 \\
(2 x-1)^2 & 0 \lt x \lt 1 \\
1 & x \geq 1
\end{array}\right.$
$\begin{aligned} & \text { When } x \gt 1 \\ & f(x)=1 \\ & f^{\prime}(x)=0\end{aligned}$
Hence, the correct answer is option: 'A'.