Q221 / 270 · NDA 2022 (Phase 1) · Mathematics

Let $y=[x+1],-4 \lt x \lt -3$ where [.] is the greatest integer function. What is the derivative of $y$ with respect to $x$ at $x=-3.5$ ?

  • A
    -4
  • B
    -3.5
  • C
    -3
  • Correct answer
    D
    0

Solution

$\begin{aligned} & \because-4 \lt \mathrm{x} \lt -3 \\ & -3 \lt \mathrm{x}+1 \lt -2 \\ & \Rightarrow[\mathrm{x}+1]=-3 \\ & \therefore \mathrm{y}=-3 \\ & \frac{\mathrm{dy}}{\mathrm{dx}}=0\end{aligned}$

Hence, the correct answer is option: 'D'.

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