APFIVE Critical Points and Differential Equations
The points $$(0, 3)$$ and $$(-1, 2)$$ are on the graph of a function $$y = f(x)$$ that satisfies the differential equation $$\displaystyle \frac{dy}{dx} = xy$$. Which of the following must be true?
A
$$(-1, 2)$$ is a critical point and $$(0, 3)$$ is not a critical point of $$f$$.
B
Neither $$(0, 3)$$ nor $$(-1, 2)$$ is a critical point of $$f$$.
C
$$(0, 3)$$ is a critical point and $$(-1, 2)$$ is not a critical point of $$f$$.
D
Both $$(0, 3)$$ and $$(-1, 2)$$ are critical points of $$f$$.
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