2.6 Related Rates (Day 2)

Objective: Find a related rate and use related rates to solve real-life problems.

Miss BattagliaAP Calculus

AP CALCULUSRELATED RATES

Related rate problems involve finding the ________ at which some variable changes.

rate

For example, when a balloon is being blown up with air, both the _____________ and the ________________ of the balloon are changing.

AP CALCULUS RELATED RATES

radiusvolume

In each case the rate is a ___________ that has to be computed given the rate at which some other variable, like time, is known to change.

AP CALCULUS RELATED RATES

derivative

To find this derivative we write an equation that relates the two variables. We then ____________

both sides of the equation with respect to ________ to express the derivative we SEEK in terms

of the derivative we KNOW.

AP CALCULUS RELATED RATES

differentiate

time

Often the key to relating the variables in this type of problem is DRAWING A PICTURE that shows the geometric relationships between the variables.

AP CALCULUS RELATED RATES

1. Identify and LABEL all the given info and what you are asked to find. Draw a picture if appropriate.

2. Write an EQUATION relating the variables.

3. Differentiate both sides of the equation with respect to TIME.

4. Substitute and Solve. Sometimes you will need to use the original equation or other equations to solve for missing parts.

Procedure:

An airplane is flying on a flight path that will take it directly over a radar tracking station. It is flying at an altitude of 6 mi, s miles from the station. If s is decreasing at a rate of 400 mi/hr when s=10 mi, what is the speed of the plane?

The Speed of an Airplane Tracked by Radar

Find the rate of change in the angle of elevation of the camera at 10 sec after lift-off.

A Changing Angle of Elevation

A camera at ground level is filming the lift-off of a space shuttle that is rising vertically according to the position equation s=50t2, where s is measured in ft and t is measured in sec. The camera is 2000 ft from the launch pad.

Oil spills in a circular pattern. The radius grows at 4 ft/min. How fast is the area of oil changing when r=10 ft.

Oil Spill

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