Problem 42E

42. (a) The curve with equation

$$

2 y^{3}+y^{2}-y^{5}=x^{4}-2 x^{3}+x^{2}

$$

has been likened to a bouncing wagon. Use a computer algebra system to graph this curve and discover why.

(b) At how many points does this curve have horizontal tangent lines? Find the $x$ -coordinates of these points.

 

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