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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2023 · Mathematics · Application of Derivatives

A function is defined by f(x)=| array ccc x+1 & 2 & 3 2 & x+4 & 6 3...

A function is defined by f(x)=\left|x+1232x+4636x+9\begin{array}{ccc} x+1 & 2 & 3 \\ 2 & x+4 & 6 \\ 3 & 6 & x+9 \end{array}\right| The function attains local minimum value at:

Options

  1. Ax=−283x=-\frac{28}{3}
  2. Bx=−1x=-1
  3. Cx=0x=0
  4. Dx=283x=\frac{28}{3}

Correct answer

C. x=0x=0

Step-by-step solution

For local minima f′(x)=0⇒3x2+28x=0⇒x=−283,0f^{\prime}(x)=0 \Rightarrow 3 x^2+28 x=0 \Rightarrow x=\frac{-28}{3}, 0 Now, f′′(x)=6x+28\quad f^{\prime \prime}(x)=6 x+28 Now, f′′(0)=28>0  and f′′(−283)>0\quad f^{\prime \prime}(0)=28 > 0 \quad \ \text{ and } \quad f^{\prime \prime}\left(\frac{-28}{3}\right) > 0 So, f(x)\mathrm{f}(\mathrm{x}) has local minimum value at x=0\mathrm{x}=0
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