Calculus, EXT1 EQ-Bank 4 MC

Which slope field best matches the differential equation \(\dfrac{d y}{d x}=-y^2\left(1- y ^2\right)\) ?

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\(C\)

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\(\text{By elimination:}\)

\(\text{At}\ \ y=0, \ \dfrac{dy}{dx}=0\ \ \text{(eliminate B)}\)

\(\text{At}\ \ y=1, \ \dfrac{dy}{dx}=-1(1-1)=0\ \ \text{(eliminate D)}\)

\(\text{At}\ \ y=-\dfrac{3}{2}, \ \dfrac{dy}{dx}=-\dfrac{9}{4}\left(1-\dfrac{9}{4}\right) \gt 0\ \ \text{(eliminate A)}\)

\(\Rightarrow C\)