3.11 Related Rates Mon 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’d Tues 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