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A curve passes through the point (2, 7/2) and has slope (1 - 1/x²) at every point (x, y) on it. What is the y-coordinate of the point on the curve whose x-coordinate is -2?
- -5/2
- 5/2
- -3/2
- 3/2
Correct answer: -3/2
Solution
Integrating gives y = x + 1/x + C; the point (2, 7/2) gives C = 1, and at x = -2, y = -2 - 1/2 + 1 = -3/2.
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