ap-calculus-bc 2000 Q5

ap-calculus-bc · USA · free-response Implicit equations and differentiation Verify implicit derivative and find tangent line features
5. Consider the curve given by $x y ^ { 2 } - x ^ { 3 } y = 6$.
(a) Show that $\frac { d y } { d x } = \frac { 3 x ^ { 2 } y - y ^ { 2 } } { 2 x y - x ^ { 3 } }$.
(b) Find all points on the curve whose $x$-coordinate is 1 , and write an equation for the tangent line at each of these points.
(c) Find the $x$-coordinate of each point on the curve where the tangent line is vertical. 
5. Consider the curve given by $x y ^ { 2 } - x ^ { 3 } y = 6$.\\
(a) Show that $\frac { d y } { d x } = \frac { 3 x ^ { 2 } y - y ^ { 2 } } { 2 x y - x ^ { 3 } }$.\\
(b) Find all points on the curve whose $x$-coordinate is 1 , and write an equation for the tangent line at each of these points.\\
(c) Find the $x$-coordinate of each point on the curve where the tangent line is vertical.\\
Paper Questions
Q2 Q3 Q4 Q5 Q6