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AP Calculus BC Full Practice Exam 4 Section II Part B

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Consider the curve defined by $$y^3=y-x^2$$. (a) Verify that $$\\frac{dy}{dx}=\\frac{2x}{1-3y^2}$$. (b) Write the equation for any horizontal tangents of the curve. (c) Write the equation for any vertical tangents of the curve. (d) At what ordered pair $$(x,y)$$ is the line $$2x+y=3$$ tangent to the curve $$y^3=y-x^2$$?

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