Bell Ringer Reminders
 Differentiation Test 2 on this Friday, 10.03.14!
 Summative Exam 1 on next Friday, 10.10.14!
Implicit Differentiation Find the derivative of the following implicitly: x3 + y2 = 5 dy/dx = 3x2 / (2y) dy/dx = 3x2 / (2y) dy/dx = 3x2 / y dy/dx = x2 / y none of the above
Find the second derivative of the following implicitly: x3 + y2 = 5 dy/dx = (12xy  9x4y1) / (4y2) dy/dx = (12xy  9x4y1) / (4y2) dy/dx = (12xy  9x4y1) / y2 dy/dx = (12xy + 9x4y1) / (4y2) none of the above
Find the equation of the tangent line at (1, 2) for the following: x3 + y2 = 5 y = ¾x + (5/4) y = ¾x  (5/4) y = ¾x + (5/4) y = ¾x  (5/4) none of the above
Related Rates Grain is poured into a conical pile at a rate of 20 ft3/min. The diameter of the base of the cone is approximately 4 times the height. At what rate is the height of the pile changing when the pile is 10 ft high? 12.5/π 0.8/π 1/(20π) 1/(2π)  none of the above
Review
 Secant vs. Tangent Line
 Definition of Derivative
 Importance of Derivative
 What does it allow us to do?
 Drawing a Tangent Line on a Graph
 Basic Differentiation Rules
 Constant Rule
 Power Rule
 Sum and Difference Rule
 Sine and Cosine Derivatives
 Derivative Notation
 Differentiation
 Rates of Change
 Position Function
 Average Velocity
 Instantaneous Velocity
 Free Fall Problems
 Product Rule
 Quotient Rule
 Chain Rule
 Implicit Differentiation
Lesson
 Related Rates
 Brainstorming Activity
 Discussion
 Checkpoints
 A  page 154 #2
 B  page 154 #16
 C  page 154 #18
 D  page 154 #20
 E  page 154 #14
Exit Ticket
 Exit Ticket will be posted on the board in class.
 Lesson Objective(s) How can differentiation be used to find the related rates?
Standard(s)  APC.5
APC.6 APC.7 APC.8 APC.9
Mathematical Practice(s)  #1  Make sense of problems and persevere in solving them
 #2  Reason abstractly and quantitatively
 #3  Construct viable arguments and critique the reasoning of others
 #4  Model with mathematics
