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Let f: R -> R be differentiable with f(0) = 0. If y = f(x) satisfies dy/dx = (2 + 5y)(5y - 2), find the value of lim (x -> infinity) f(x).
- -2/5
- 2/5
- 0
- 5/2
Correct answer: -2/5
Solution
The equilibria are y = +/-2/5; starting at y(0)=0 the slope is negative, so f decreases toward the stable equilibrium y = -2/5.
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