TS EAMCET · Maths · Application of Derivatives
If the function \(\int(x)=\frac{x}{5}+\frac{5}{x},(x \neq 0)\) attains its relative maximum value at \(\mathrm{x}=a\) then \(\sqrt{a^2+2 a-6}=\)
- A \(10\)
- B \(6\)
- C \(5\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=\frac{x}{5}+\frac{5}{x}=\frac{x^2+25}{5 x} \\ & f^{\prime}(x)=\frac{5 x(2 x)-\left(x^2+25\right)(5)}{(5 x)^2} \\ & \Rightarrow f^{\prime}(x)=\frac{x^2-25}{5 x^2} \\ & \text { when } f^{\prime}(x)=0 \Rightarrow x^2-25=0 \Rightarrow x= \pm 5 \\ & \text { for…
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