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The Curve Graphed Below Has Equation 2y3+y2y5=x42x3+x22 y ^ { 3 } + y ^ { 2 } - y ^ { 5 } = x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 }

Question 138

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The curve graphed below has equation 2y3+y2y5=x42x3+x22 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 dydx\frac { d y } { d x } .
b)Find the slope of the tangent line at the point (1, -1).  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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