AP Calculus BC
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Derivatives Quiz: Implicit and Inverses Name:
9-11-15
Given the relation (x 2 + y 2 )2 = 2x 2 - 2y 2 (as shown).
dy
x(1- x 2 - y 2 )
.
=
dx y(x 2 + y 2 + 1)
a.
Show
b.
Find all points of horizontal tangency. (Note: There should be four such points.)
The curve x 3 + y 3 = 4xy is known as the Folium of Descartes.
a.
Use the implicit grapher link on my website to sketch the curve.
b.
Find an equation of the tangent line to the curve at the point (2, 2).
c.
Find all points of horizontal tangency.
d.
Find all points of vertical tangency.
Consider the curve given by xy 2 - x 3y = 6 .
a.
Use the implicit grapher link on my website to sketch the curve.
b.
Find all points of horizontal tangency.
c.
Find all points of vertical tangency.
d.
Solve the equation for y. Using limits, explain informally, yet thoroughly, why lim f (x,y) = lim f (x,y) = 0 .
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