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Explain solution RD Sharma class 12 Chapter 17 Maxmima and Minima Exercise Case Study Questions question 7 subquestion (iii)

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Answer:  \frac{25600}{\left(x^{2}-25600\right)^{3 / 2}}

Hint: use the concept of maxima and minima.


\begin{aligned} \frac{d y}{d x} &=2-\frac{x}{\sqrt{x^{2}-25600}} \\ \end{aligned}

\qquad \begin{aligned} \frac{d^{2} y}{d x^{2}} &=-\left[\frac{1}{\sqrt{\left(x^{2}-25600\right)}}+x \cdot \frac{-1}{2\left(x^{2}-25600\right)^{\frac{3}{2}}} \cdot 2 x\right] \\ \end{aligned}

=\left[\frac{25600}{\left(x^{2}-25600\right)^{3 / 2}}\right]

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