Update
 Unit 2b Test next Tuesday, 02.24
Bell Ringer
Find when x = 1, given that when x = 1. 0 1 2 4 none of the above
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area A of the disturbed water changing? 8
4
 none of the above
Review
 Prerequisite
 Secant Lines (video)
 Tangent Lines (video)
 Equation of a Tangent Line (video)
 Derivative (video)
Lesson
Exit Ticket
 Posted on the board at the end of the block
 Lesson Objectives
 How is implicit differentiation used to solve problems?
Standard(s)
 APC.5
 Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.
 The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.
 APC.6
 The student will investigate the derivative at a point on a curve.
 Includes:
 finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangents
 using local linear approximation to find the slope of a tangent line to a curve at the point
 defining instantaneous rate of change as the limit of average rate of change
 approximating rate of change from graphs and tables of values.
 APC.7
 Analyze the derivative of a function as a function in itself.
 Includes:
 comparing corresponding characteristics of the graphs of f, f', and f''
 defining the relationship between the increasing and decreasing behavior of f and the sign of f'
 translating verbal descriptions into equations involving derivatives and vice versa
 defining the relationship between the concavity of f and the sign of f "
 APC.9
 Apply formulas to find derivatives.
 Includes:
 derivatives of algebraic and trigonometric functions
 derivations of sums, products, quotients, inverses, and composites (chain rule) of elementary functions
 derivatives of implicitly defined functions
 higher order derivatives of algebraic and trigonometric functions
Past Checkpoints  Derivative
 Derivative Rules
 Higher Order Derivatives
 Rates of Change
 Position Function
 Velocity Function
 Acceleration Function
 Product Rule
 Quotient Rule
 Chain Rule
 Implicit Differentiation
 Related Rates
