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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2022 · Mathematics · Application of Derivatives

If the derivative of the function f(x)=(m)/(x)+2 n x+1 vanishes at...

If the derivative of the function f(x)=mx+2nx+1f(x)=\frac{m}{x}+2 n x+1 vanishes at x=2x=2, then what is the value of m+8n?m+8 n ?

Options

  1. A-2
  2. B0
  3. C2
  4. DCannot be determined due to insufficient data

Correct answer

D. Cannot be determined due to insufficient data

Step-by-step solution

F(x)=mx+2nx+1∴\mathrmf′(x)=−mx2+2n\begin{aligned} & \mathrm{F}(\mathrm{x})=\frac{\mathrm{m}}{\mathrm{x}}+2 \mathrm{nx}+1 \\ & \therefore \mathrmf^{\prime}(\mathrm{x})=\frac{-\mathrm{m}}{\mathrm{x}^2}+2 \mathrm{n}\end{aligned} given that f′(2)=0f^{\prime}(2)=0∴−m(2)2+2n=0−m+8n=0\begin{aligned} & \therefore \frac{-\mathrm{m}}{(2)^2}+2 \mathrm{n}=0 \\ & -\mathrm{m}+8 \mathrm{n}=0\end{aligned}⇒8n−m=0\Rightarrow 8 \mathrm{n}-\mathrm{m}=0...(i) from equation we can't find value of m+8nm+8 n.
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