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A curve goes through the point (2, 7/2). At any point (x, y) on the curve, its slope is given by 1 - 1/x². What is the y-coordinate of the point on this curve whose x-coordinate is -2?
- -3/2
- 3/2
- 5/2
- -5/2
Correct answer: -3/2
Solution
Integrating dy/dx = 1 - 1/x^2 gives y = x + 1/x + C. Using y(2)=7/2: 2+1/2+C=7/2 -> C=1. At x=-2: y = -2 - 1/2 + 1 = -3/2.
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