Critical Points and Differential Equations

Question

The function $$y=f(x)$$ is a solution to the differential equation $$\displaystyle \frac{dy}{dx} = xy$$, and its graph passes through the points $$(0, 3)$$ and $$(-1, 2)$$. Which of the following statements must be true?

Accepted Answer

$$(0, 3)$$ is a critical point and $$(-1, 2)$$ is not a critical point of $$f$$.

Answer

Neither $$(0, 3)$$ nor $$(-1, 2)$$ is a critical point of $$f$$.

Answer

$$(-1, 2)$$ is a critical point and $$(0, 3)$$ is not a critical point of $$f$$.

Answer

Both $$(0, 3)$$ and $$(-1, 2)$$ are critical points of $$f$$.

Critical Points and Differential Equations

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