APFIVE Slope of a Solution Curve
The points $$(0, 0)$$ and $$(1, 1)$$ are on the graph of a function $$y = f(x)$$ that satisfies the differential equation $$\displaystyle \frac{dy}{dx} = x^2 + y^2$$. Which of the following must be true?
A
Both points are critical points of $$f$$.
B
The graph of $$f$$ has slope 1 at both points.
C
The function $$f$$ is decreasing at both points.
D
The graph of $$f$$ has a horizontal tangent line at $$(0, 0)$$ and slope 2 at $$(1, 1)$$.
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