The minimum distance between the origin and the curve y = x² + 2 is:
The minimum distance between the origin and the curve y = x² + 2 is:
- A. √2
- B. 2
- C. √3
- D. 1
Answer: A) √2
Explanation: Distance squared D = x² + (x² + 2)² = x² + x⁴ + 4x² + 4 = x⁴ + 5x² + 4. dD/dx = 4x³ + 10x = 2x(2x² + 5) = 0 → x = 0. D(0) = 4, min distance = 2.
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