CUET · MATHS · PYQ PAPER 2023
The minimum value of \(\left(x^2+\frac{250}{x}\right)\) is :
- A 25
- B 50
- C 75
- D 85
Answer & Solution
Correct Answer
(C) 75
Step-by-step Solution
Detailed explanation
\(f(x) = x^2 + 250x^{-1}\) \(f'(x) = 2x - 250x^{-2}\) \(2x - \frac{250}{x^2} = 0 \Rightarrow 2x^3 = 250 \Rightarrow x^3 = 125 \Rightarrow x = 5\) \(f(5) = 5^2 + \frac{250}{5}\) \(f(5) = 25 + 50 = 75\)
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