Section 3 9 Related Rates AP Calculus October

Section 3. 9 Related Rates AP Calculus October 15, 2009 Berkley High School, D 2 B 2 todd 1@toddfadoir. com Calculus, Section 3. 9

More variation on notation Calculus, Section 3. 9 2

More variation on notation Calculus, Section 3. 9 3

Why this is important n n The ability to take the derivative “with respect to time”, allows to look at rates of change which are time based These rates include velocity, growth or decay Calculus, Section 3. 9 4

Example n Air is being pumped into a spherical balloon at a rate of 100 cm 3/s. How fast is the radius changing when the radius is 25 cm? ¨ What do we know? ¨ What don’t we know? Calculus, Section 3. 9 5

Example n n Air is being pumped into a spherical balloon at a rate of 100 cm 3/s. How fast is the radius changing when the radius is 25 cm? Calculus, Section 3. 9 6

Example Calculus, Section 3. 9 7

Example n A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall? ¨ Draw a diagram first, and define your variables. Calculus, Section 3. 9 8

Example n A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall? 10 y Calculus, Section 3. 9 x 9

Example n n What do we know? What don’t we know? 10 y x Calculus, Section 3. 9 10

Example n n What do we know? What don’t we know? Calculus, Section 3. 9 11

Assignment Section 3. 9, 1 -17, odd n Section 3. 9, 19 -25, odd tomorrow n Calculus, Section 3. 9 12

Calculus, Section 3. 9 13

Calculus, Section 3. 9 14