Question

The function \(f(x)=\dfrac{x}{2}+\dfrac{2}{x}\) has local minimum at

• A. \(x=2\)
• B. \(x=-2\)
• C. \(x=0\)
• D. \(x=1\)

Hint:

Check second derivative for extrema type.

Answer 1

The Correct Option is A

Step 1: \[ f'(x)=\frac12-\frac{2}{x^2} \Rightarrow x^2=4 \]
Step 2: \[ f''(x)=\frac{4}{x^3} \]
Step 3: \(f''(2) > 0\Rightarrow\) minimum at \(x=2\).