Name __________________________________
Calculus:
Practice Test for 3.5- 3.7: Chain Rule, Implicit Differentiation, Related Rates
1. Find
for
2.
3. Find
4. Find the
for
and
for the equation
5. The Folium of Descartes is a curve described by the equation
a) Find y’
b) Find the equation of the tangent line to the curve at (3,3)
6. If a snowball melts so the surface area decreases at a rate of 1
, find the rate
at which the diameter decreases when the diameter is 10 cm.
7. Two cars start moving from the same point. One travels south at 60 miles/hour
and the other travels west at 25 miles/hour. At what rate is the distance between
the cars increasing two hours later?
8. A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks
from the spotlight towards the building at a speed of 1.6 m/sec, how fast is the
length of the shadow on the building changing when he is 4 m from the building?
9. A water tank has the shape of an inverted circular cone with base radius of 2 feet
and a height of 4 feet. If water is being pumped into the tank at a rate of 2
,
find the rate at which the water level is rising when the water is 3m deep.
10. Water is leaking out of an inverted conical tank at a rate of 10,000
at the
same time that water is being pumped into the tank at a constant rate. The tank
has a height of 6 meters and a diameter at the top of 4 meters.
If the water level is rising at a rate of 20 cm/min when the height is 2 m, find the
rate at which the water is being pumped into the tank.