Local Extrema on a Solution Curve

Question

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?

Accepted Answer

$$(1, 1)$$ is a local maximum and $$(-1, 1)$$ is a local minimum of $$f$$.

Answer

Both points are inflection points of the graph of $$f$$.

Answer

Both $$(1, 1)$$ and $$(-1, 1)$$ are local maxima of $$f$$.

Answer

Both $$(1, 1)$$ and $$(-1, 1)$$ are local minima of $$f$$.

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	minhkhangchatchoi2008	1	1	0m 03s	97
#2	charlie.long.vn	2	2	2m 51s	29
#3	kamalkaren31	1	2	1m 51s	-21
#4	yeejayc	0	1	1m 08s	-78

Local Extrema on a Solution Curve

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