COMEDK · Maths · 27. Application of Derivatives
The function \(f(x)=\dfrac{x}{2}+\dfrac{2}{x}\) has a local minimum at
- A \(x=2\)
- B \(x=0\)
- C \(x=-2\)
- D \(x=1\)
Answer & Solution
Correct Answer
(A) \(x=2\)
Step-by-step Solution
Detailed explanation
Given the function \(f(x) = \dfrac{x}{2} + \dfrac{2}{x}\). To find the local extrema, calculate the first derivative \(f'(x)\): \(f'(x) = \dfrac{d}{dx} \left( \dfrac{x}{2} + 2x^{-1} \right) = \dfrac{1}{2} - 2x^{-2} = \dfrac{1}{2} - \dfrac{2}{x^2}\). Set \(f'(x) = 0\) to find the…
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