AP EAMCET · Maths · Differentiation
If \(f(x)=\sqrt{x+2 \sqrt{2 x-4}}+\sqrt{x-2 \sqrt{2 x-4}}\), then the value of \(10 \times f^{\prime}(102)=\)
- A 1
- B 2
- C 102
- D -1
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} f(x)= & \sqrt{x+2 \sqrt{2 x-4}}+\sqrt{x-2 \sqrt{2 x-4}} \\ = & \sqrt{(x-2)+2+2 \sqrt{2} \sqrt{x-2}} \\ & \quad+\sqrt{(x-2)+2-2 \sqrt{2} \sqrt{x-2}} \\ & =|\sqrt{x-2}+\sqrt{2}|+|\sqrt{x-2}-\sqrt{2}| \end{aligned}\) for \(x \geq 4\)…
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