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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differentiation

NDA 2013 · Mathematics · Differentiation

If y= (a x+b) , then what is (d^2 y)/(d x^2) at x=-(b)/(a) , where...

If y=sin⁡(ax+b)y=\sin (a x+b), then what is d2ydx2\frac{d^2 y}{d x^2} at x=−bax=-\frac{b}{a}, where a,ba, b are constants and a≠0a \neq 0 ?

Options

  1. A00
  2. B−1-1
  3. Csin⁡(a−b)\sin (a-b)
  4. Dsin⁡(a+b)\sin (a+b)

Correct answer

A. 00

Step-by-step solution

dydx=acos⁡(ax+b)d2ydx2=−a2sin⁡(ax+b)=−a2sin⁡(0)=0\begin{aligned} & \frac{d y}{d x}=a \cos (a x+b) \\ & \frac{d^2 y}{d x^2}=-a^2 \sin (a x+b)=-a^2 \sin (0)=0\end{aligned}
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