The Curve Graphed Below Has Equation $2 y ^ { 3 } + y ^ { 2 } - y ^ { 5 } = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 }$

question 68

Essay

The curve graphed below has equation $2 y ^ { 3 } + y ^ { 2 } - y ^ { 5 } = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 }$ .It is called the "bouncing wagon curve."
a)Use implicit differentiation to find $\frac { d y } { d x }$ .
b)Find the slope of the tangent line at the point (1, -1).

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