Function Behavior From a Differential Equation

Question

A function $$y=f(x)$$ satisfies the differential equation $$\frac{dy}{dx}=x-y$$. If the graph of $$f$$ contains the points $$(1,1)$$ and $$(2,3)$$, which of the following must be true?

Accepted Answer

The function $$f$$ has a horizontal tangent at $$(1, 1)$$ and is decreasing at $$(2, 3)$$.

Answer

The function $$f$$ is increasing at both points.

Answer

The function $$f$$ is decreasing at $$(1, 1)$$ and increasing at $$(2, 3)$$.

Answer

The function $$f$$ is increasing at $$(1, 1)$$ and decreasing at $$(2, 3)$$.

Function Behavior From a Differential Equation

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