Concavity of a Solution Curve

Question

Let $$y = f(x)$$ be a solution to the differential equation $$\frac{dy}{dx} = y - x$$. Which of the following statements must be true concerning the concavity of the graph of $$f$$ at the points $$(0, 2)$$ and $$(2, 2)$$?

Accepted Answer

The graph of $$f$$ is concave up at $$(0, 2)$$ and concave down at $$(2, 2)$$.

Answer

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

Answer

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

Answer

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

Concavity of a Solution Curve

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