Presentation is loading. Please wait.

Presentation is loading. Please wait.

4.6: Related Rates Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts.

Published byAlan Smith Modified over 6 years ago

Similar presentations

Presentation on theme: "4.6: Related Rates Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts."— Presentation transcript:

1 4.6: Related Rates Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts

2 What should we do when two connected variables each depend on a different variable?? How can we incorporate rate-of-change information?

3 The sphere is growing at a rate of .
Suppose that the radius of a sphere is changing at an instantaneous rate of 0.1 cm per second (a soap bubble or a balloon.) How fast is the volume changing when the radius is 10 cm? (Aren’t you glad you remember the Chain Rule and implicit differentiation?) The sphere is growing at a rate of Note: This is an exact result!

4 Water is draining from a cylindrical tank at 3 liters/second.
How fast is the water’s surface dropping if the radius is constant? Find (We need a formula to relate V and h. ) (r is a constant.)

5 Steps for Related Rates Problems:
1. Draw a diagram (sketch). 2. Write down known information. 3. Write down the rate you are looking for. Write an equation to relate the variables in the rates involved. 5. Differentiate both sides with respect to t. Evaluate the rates if there is a particular time value!

6 Hot Air Balloon Problem:
Given: How fast is the balloon rising when the base angle is π/4 radians? Find a formula to relate θ and h! Find

7 Hot Air Balloon Problem:
Given: How fast is the balloon rising? Find

8 Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr.
Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later? B A

9 Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr.
Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later? B A

10 Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr.
Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later? B A

Download ppt "4.6: Related Rates Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts."

Similar presentations

2.6 Related Rates.

2.6 Related Rates.
4.4 Optimization Buffalo Bills Ranch, North Platte, Nebraska Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin,

4.4 Optimization Buffalo Bills Ranch, North Platte, Nebraska Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin,
3.3 Differentiation Rules

3.3 Differentiation Rules
3.1 Derivatives Great Sand Dunes National Monument, Colorado Photo by Vickie Kelly, 2003 Created by Greg Kelly, Hanford High School, Richland, Washington.

3.1 Derivatives Great Sand Dunes National Monument, Colorado Photo by Vickie Kelly, 2003 Created by Greg Kelly, Hanford High School, Richland, Washington.
3.4 Velocity, Speed, and Rates of Change Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover,

3.4 Velocity, Speed, and Rates of Change Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover,
3.6 The Chain Rule Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts Photo.

3.6 The Chain Rule Created by Greg Kelly, Hanford High School, Richland, Washington Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts Photo.
Related Rates Chapter 3.7. Related Rates The Chain Rule can be used to find the rate of change of quantities that are related to each other The important.

Related Rates Chapter 3.7. Related Rates The Chain Rule can be used to find the rate of change of quantities that are related to each other The important.
4.6: Related Rates. First, a review problem: Consider a sphere of radius 10cm. If the radius changes 0.1cm (a very small amount) how much does the volume.

4.6: Related Rates. First, a review problem: Consider a sphere of radius 10cm. If the radius changes 0.1cm (a very small amount) how much does the volume.
Teresita S. Arlante Naga City Science High School.

Teresita S. Arlante Naga City Science High School.
2.7 Related Rates.

2.7 Related Rates.
When we first started to talk about derivatives, we said that becomes when the change in x and change in y become very small. dy can be considered a very.

When we first started to talk about derivatives, we said that becomes when the change in x and change in y become very small. dy can be considered a very.
DERIVATIVES 3. 3.8 Related Rates In this section, we will learn: How to compute the rate of change of one quantity in terms of that of another quantity.

DERIVATIVES Related Rates In this section, we will learn: How to compute the rate of change of one quantity in terms of that of another quantity.
2.8 Related Rates.

2.8 Related Rates.
Review Problem: Use implicit differentiation to find If.

Review Problem: Use implicit differentiation to find If.
Related Rates Section 4.6a.

Related Rates Section 4.6a.
3.9 Related Rates 1. Example Assume that oil spilled from a ruptured tanker in a circular pattern whose radius increases at a constant rate of 2 ft/s.

3.9 Related Rates 1. Example Assume that oil spilled from a ruptured tanker in a circular pattern whose radius increases at a constant rate of 2 ft/s.
Olympic National Park, Washington Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007 4.6: Related Rates.

Olympic National Park, Washington Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, : Related Rates.
Calculus warm-up Find. xf(x)g(x)f’(x)g’(x) 318-3-5 63-245 834 12-650 For each expression below, use the table above to find the value of the derivative.

Calculus warm-up Find. xf(x)g(x)f’(x)g’(x) For each expression below, use the table above to find the value of the derivative.
Warmup 1) 2). 4.6: Related Rates They are related (Xmas 2013)

Warmup 1) 2). 4.6: Related Rates They are related (Xmas 2013)
Related Rates 3.7. Finding a rate of change that cannot be easily measured by using another rate that can be is called a Related Rate problem. Steps for.

Related Rates 3.7. Finding a rate of change that cannot be easily measured by using another rate that can be is called a Related Rate problem. Steps for.

Similar presentations

Ads by Google