S ECTION 3.6 R ECAP Derivatives of Inverse Functions

O UR M AIN F OCUS

A DDITIONAL 3.6 E XAMPLE

W HAT W E ’ VE L EARNED T HUS F AR

S ECTION 3.7 Related Rates

When water is drained out of a conical tank the volume V, the radius r, and the height h of the water level are all functions of time t.

E XAMPLE 1 A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area A of the disturbed water changing.

E XAMPLE 2 Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate of change of the radius when the radius is 2 feet.

E XAMPLE 3 EquationFindGiven

E XAMPLE 4 Equation x- value

E XAMPLE 5

E XAMPLE 6 All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is 10 centimeters?

E XAMPLE 7 Using example 6, how fast is the surface area changing when each edge is 10 cm?

E XAMPLE 8 A conical tank with vertex down is 10 ft. across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic ft. per minute, find the rate of change of the depth of the water when the water is 8 ft. deep.

E XAMPLE 9

S UMMARY

C ONCEPT C HECK

Q UESTIONS ? Remember to be working the practice problems.