APFIVE Local Extrema on a Solution Curve
A function $$y=f(x)$$ is a solution to the differential equation $$\displaystyle \frac{dy}{dx} = y - x^2$$. If the graph of $$f$$ passes through the points $$(1, 1)$$ and $$(-1, 1)$$, which of the following statements must be true?
A
$$(1, 1)$$ is a local maximum and $$(-1, 1)$$ is a local minimum of $$f$$.
B
Both $$(1, 1)$$ and $$(-1, 1)$$ are local minima of $$f$$.
C
Both points are inflection points of the graph of $$f$$.
D
Both $$(1, 1)$$ and $$(-1, 1)$$ are local maxima of $$f$$.
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