Tangent Line Slope From a Differential Equation

Question

The points $$(0, 2)$$ and $$(2, 0)$$ lie on the graph of a function $$y = f(x)$$ that is a solution to the differential equation $$\frac{dy}{dx} = 2xy$$. Which of the following statements must be true?

Accepted Answer

The function $$f$$ has a horizontal tangent line at $$(0, 2)$$.

Answer

The function $$f$$ has a vertical tangent line at $$(2, 0)$$.

Answer

The function $$f$$ is decreasing at both given points.

Answer

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

Tangent Line Slope From a Differential Equation

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