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
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