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3.11 Related Rates Mon Nov 10PowerPoint Presentation

3.11 Related Rates Mon Nov 10

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3.11 Related RatesMon Nov 10

- Do Now
- Differentiate implicitly in terms of t
- 1)
- 2)

Related Rates

- When we use implicit differentiation, we obtain dy/dx, or the change of y in terms of x.
- In many real life situations, each quantity in an equation changes with time (or another variable)
- In this case, any derivative we find is called a related rate, since each rate in the derivative is related to each other

Related Rates Steps

- 1) Make a simple sketch, if possible
- 2) Identify what rate you are looking for
- 3) Set up an equation relating ALL of the relevant quantities
- 4) Differentiate both sides of the equation in terms of the variable you want
- if you want dv/dt, you differentiate in terms of t

- 5) Substitute in values we know
- 6) Solve for the remaining rate

Ex 1

- A 5-meter ladder leans against a wall. The bottom of the ladder is 1.5 m from the wall at time t=0 and slides away from the wall at a rate of 0.8m/s. Find the velocity of the top of the ladder at time t=1

Ex 2

- Water pours into a fish tank at a rate of 0.3 m^3 / min. How fast is the water level rising if the base of the tank is a rectangle of dimensions 2 x 3 meters?

Ex 3

- Water pours into a conical tank of height 10 m and radius 4 m at a rate of 6 m^3/min
- A) At what rate is the water level rising when the level is 5 m high?
- B) As time passes what happens to the rate at which the water level rises?

Ex 4

- A spy uses a telescope to track a rocket launched vertically from a launching pad 6km away. At a certain moment, the angle between the telescope and ground is equal to pi/3 and is changing at a rate of 0.9 radians/min. What is the rocket’s velocity at that moment?

Ex 5

- See book

Closure

- At what rate is the diagonal of a square increasing if its sides are increasing at a rate of 2 cm/s?
- HW: p.199 #1-37 every other odd
- Ch 3 Test next week? Mon?

3.11 Related Rates Cont’dTues Nov 11

- Do Now
- Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 10 cm.
- (hint: Volume = 4/3 pi x r^3)

HW Review p.199 #1-35

- Probably all of them

More practice

- worksheet

Closure

- Hand in: A 15 foot ladder is resting against the wall. The bottom is initially x feet away from the wall and is being pushed towards the wall at a rate of 0.5 ft/sec. How fast is the top of the ladder moving up the wall when the bottom of the ladder is 4 feet from the wall?? (Hint: Use Pythagorean Theorem)
- HW: p.199 #1-35 all other odd
- p.AP3-1 #1-20, 1-4 due Thurs
- P.203 #5-11, 17-25, 29-75 85-115 119-123 due Fri

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