Related Rates AP Calculus October 21 24 2019

Related Rates AP Calculus October 21 -24, 2019 Mrs. Agnew

Essential Stuff Essential Question 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

Finding Related Rates l We have seen how implicit differentiation can be used to find derivatives of implicit relations. l 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. l Since we are differentiating with respect

Example Given that x and y are both differentiable functions of t and y = x 2 + 3. Find dx/dt when x = 1, given that dy/dt = 2. Larson Text: page 154 #2 -8

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

Related Rate Problems l Related rate word problems have two quantities based on time… l l l Radius and area Volume and length Angle of elevation and length Two sides of a (right) triangle Guided Practice: l Rogawski Text – 3. 11

Homework Page 269 – 271 #4, 5 – 15 (Odd), 19, 21, 25, 29