Draw a picture to model problem.
Label given information.
Identify what you are solving for in
the problem.
Write an equation that relates the
given information.
Differentiate your equation.
Evaluate the derivative using the
given information.
Water pours into a fish tank at a rate of
0.3m3/min. How fast is the water level rising if
the base of the tank is a rectangle of
dimensions 2x3 meters?
A spy uses a telescope to track a rocket launched
vertically from a launching pad 6 km away. At a
certain moment, the angle between the telescope and
the ground is equal to π/3 and is changing at a rate of
0.9 rad/min. What is the rocket’s velocity at that
moment?
A plane is flying at 450 km/hr at a constant altitude of 5
km and is approaching a camera mounted on the
ground. Let θ be the angle at which the camera is
pointed. When θ=Π/3 how fast does the camera have to
rotate to keep the plane in view?
Water runs into a conical tank at the rate of 9 cubic feet
per minute. The tank stands point down and has a
height of 10 feet and a base radius of 5 feet. How fast is
the water level rising when the water is 6 feet deep?
A 13-foot ladder is leaning against a house when its
base starts to slide away. By the time the base is 12 feet
from the house, the base is moving at the rate of 5 feet
per second. How fast is the top of the ladder sliding
down the wall then? At what rate is the area of the
triangle formed by the ladder, wall, and ground
changing then? At what rate is the angle between the
ladder and the ground changing then?
Coffee is draining from a conical filter (radius of 3 feet and
height of 6 feet) into a cylindrical coffeepot (radius of 3 feet)
at the rate of 10 cubic inches per minute. How fast is the
level in the pot rising when the coffee in the cone is 5 inches?
How fast is the level in the cone falling then?
A spherical iron ball 9 inches in diameter is coated with a layer
of ice of uniform thickness. If the ice melts at the rate of 10
cubic inches per minute, how fast is the thickness of the ice
decreasing when it is 2 inches thick? How fast is the outer
surface area of ice decreasing?
Homework
Section 3.4
Pg. 209-211 problems 1-47 eoo.