APFIVE Slope of a Solution Curve
The graph of a particular solution to the differential equation $$\displaystyle \frac{dy}{dx} = x - y$$ passes through the points $$(1, 1)$$ and $$(2, 3)$$. Which of the following must be true?
A
The function $$f$$ is decreasing at $$(1, 1)$$ and increasing at $$(2, 3)$$.
B
The function $$f$$ has a horizontal tangent at $$(1, 1)$$ and is decreasing at $$(2, 3)$$.
C
The function $$f$$ is increasing at $$(1, 1)$$ and decreasing at $$(2, 3)$$.
D
The function $$f$$ is increasing at both points.
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