Math 201: Implicit Differentiation Day 26
Put your calculator away.
(1) For the following curves compute
i. the derivative dy
dx
ii. the equation of the tangent line at all points of the form (x, 0)
(a) x2y+ 2xy2
−3 = x+y
(b) exy =x2+y2
(2) Find all points where the tangent line to the curve (x2+y2)2= 4(x2
−y2) is horizontal.
(3) Assume that both xand yare functions of time, t. Implicitly differentiate the equation
x2+y2= 50 with respect to time.
(4) The volume of a cone is V=1
3πr2h. Assume that both the height and radius are functions
of time, t.
(a) Implicitly differentiate this equation with respect to time, t.
(b) If the units are centimeters and seconds and the radius changes at a rate of 3 cm per
second, and the height changes at a rate of 5 cm per second, how fast is the volume
changing?
1