APFIVE Concavity from a Differential Equation
The points $$(-1, 0)$$ and $$(2, -1)$$ are on the graph of a function $$y = f(x)$$ that satisfies the differential equation $$\displaystyle \frac{dy}{dx} = x + y$$. Which of the following must be true?
A
Both points are inflection points of the graph of $$f$$.
B
$$(-1, 0)$$ is an inflection point and the graph is concave up at $$(2, -1)$$.
C
The graph of $$f$$ is concave down at both points.
D
The graph of $$f$$ is concave up at both points.
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