Slope of a Solution Curve

Question

The graph of the function $$y = f(x)$$ passes through the points $$(0, 0)$$ and $$(1, 1)$$ and is a solution to the differential equation $$\displaystyle \frac{dy}{dx} = x^2 + y^2$$. Which of the following must be true?

Accepted Answer

The graph of $$f$$ has a horizontal tangent line at $$(0, 0)$$ and slope 2 at $$(1, 1)$$.

Answer

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

Answer

The graph of $$f$$ has slope 1 at both points.

Answer

Both points are critical points of $$f$$.

Slope of a Solution Curve

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