Concavity from a Differential Equation

Question

Let $$y=f(x)$$ be a function that is a solution to the differential equation $$\displaystyle \frac{dy}{dx} = x + y$$. If the graph of $$f$$ passes through the points $$(-1, 0)$$ and $$(2, -1)$$, which of the following statements about the graph of $$f$$ must be true?

Accepted Answer

$$(-1, 0)$$ is an inflection point and the graph is concave up at $$(2, -1)$$.

Answer

The graph of $$f$$ is concave down at both points.

Answer

The graph of $$f$$ is concave up at both points.

Answer

Both points are inflection points of the graph of $$f$$.

Concavity from a Differential Equation

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