Related Rates OBJ: Solve related rates problem scenarios

Related Rates are…. Usually Dependent on Time

Ex 1: Finding equations Let V = 4/3πr 3 be the volume of a sphere dependent on time. Find dV/dt

Strategies to Solve 1. Identify primary and secondary info 2. Develop a model/Draw picture 3. Write equations for primary and secondary 4. Get primary into one variable (if possible) ((This can only be done if other info is CONSTANT)) 5. Implicitly differentiate 6. Substitute values 7. Interpret solutions (with correct units)

Ex 1: p 251 #11 A spherical balloon is inflated with helium at the rate of 100π ft 3 /min. How fast is the balloon’s radius increasing at the instant the radius is 5?

Ex 1

Ex 2: p. 251 #14 Shante flies a kite at a height of 300 ft, the wind carrying the kite horizontally away at a rate of 25 ft/sec. How fast must she let out the string when the kite is 500 ft away from her?

Ex 2

Example 3 A rectangle’s area is increasing at a rate of 20 ft 2 /min and its width is decreasing at a rate of 3 ft/min. How fast is the length changing when the width is 4 ft?

Example 3 Con’t.d

TO DO: 1) CW:Setting Up-Related Rates 2) HW: Each Spring