1. AP Calculus March 6-7, 2017 Mrs. Agnew
Related Rates
AP Calculus
March 6-7, 2017
Mrs. Agnew

2. Essential Stuff Essential Question Essential Vocabulary
How do you find the rate of change of a quantity when multiple quantities are changing with respect to time?
Essential Vocabulary
Related Rates
Implicit Differentiation
Rate of Change

3. Finding Related Rates
We have seen how implicit differentiation can be used to find derivatives of implicit relations.
Implicit differentiation can also be used to find the rate of change of two (or more) related variables that are changing with respect to time.
Since we are differentiating with respect to time, we write dx/dt AND dy/dt.
Animation

4. Example Given that x and y are both differentiable
functions of t and y = x Find dx/dt
when x = 1, given that dy/dt = 2.
Larson Text: page 154 #2-8 (E)

5. Related Rates Problems
List everything you know and draw a diagram…
Value(s) of variable(s) and Rates of Change
Identify quantities that do NOT change and quantities that do change.
Write equation involving all variables either given or to be determined.
Differentiate, plug in given values, and solve
Animated Example

6. Related Rate Problems
Related rate word problems have two quantities based on time…
Radius and area
Volume and length
Angle of elevation and length
Two sides of a (right) triangle
Guided Practice:
Rogawski Text – 3.11

7. Homework
Page 269 – 271
#4, 5 – 21 (Odd), 25, 29