ap-calculus-ab 1998 Q6

ap-calculus-ab · USA · full-exam Tangents, normals and gradients Verify implicit derivative and find tangent line features

6. Consider the curve defined by $2 y ^ { 3 } + 6 x ^ { 2 } y - 12 x ^ { 2 } + 6 y = 1$.
(a) Show that $\frac { d y } { d x } = \frac { 4 x - 2 x y } { x ^ { 2 } + y ^ { 2 } + 1 }$.
(b) Write an equation of each horizontal tangent line to the curve.
(c) The line through the origin with slope - 1 is tangent to the curve at point $P$. Find the $x$ - and $y$-coordinates of point $P$.

6. Consider the curve defined by $2 y ^ { 3 } + 6 x ^ { 2 } y - 12 x ^ { 2 } + 6 y = 1$.\\
(a) Show that $\frac { d y } { d x } = \frac { 4 x - 2 x y } { x ^ { 2 } + y ^ { 2 } + 1 }$.\\
(b) Write an equation of each horizontal tangent line to the curve.\\
(c) The line through the origin with slope - 1 is tangent to the curve at point $P$. Find the $x$ - and $y$-coordinates of point $P$.

Paper Questions

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