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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2022 · Mathematics · Continuity and Differentiability

Let y=[x+1],-4 < x < -3 where [.] is the greatest integer function....

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

Options

  1. A-4
  2. B-3.5
  3. C-3
  4. D0

Correct answer

D. 0

Step-by-step solution

∵−4<x<−3−3<x+1<−2⇒[x+1]=−3∴y=−3dydx=0\begin{aligned} & \because-4 < \mathrm{x} < -3 \\ & -3 < \mathrm{x}+1 < -2 \\ & \Rightarrow[\mathrm{x}+1]=-3 \\ & \therefore \mathrm{y}=-3 \\ & \frac{\mathrm{dy}}{\mathrm{dx}}=0\end{aligned}
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