Local Extrema of a Differential Equation Solution

Question

Let $$y = f(x)$$ be a solution to the differential equation $$\displaystyle \frac{dy}{dx} = x^2 + y$$. If the graph of $$f$$ passes through the points $$(-1, -1)$$ and $$(1, -5)$$, which of the following must be true?

Accepted Answer

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

Answer

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

Answer

$$(1, -5)$$ is a local maximum of $$f$$.

Answer

$$(1, -5)$$ is a point of inflection of the graph of $$f$$.

Local Extrema of a Differential Equation Solution

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