Bell Ringer
Find the derivative of the following:  
none of the above
Find the second derivative (derivative of the derivative) of the following:  
none of the above
Find the point(s) at which the following function has a horizontal tangent line:  
none of the above
Find the derivative of the following function:  
none of the above
Find the derivative of the following function:  
- none of the above
Review
- Prerequisite
- Secant Lines (video)
- Tangent Lines (video)
- Equation of a Tangent Line (video)
- Derivative (video)
- Derivative Rules
- Constant Rule (video)
- Power Rule (video)
- Constant Multiple Rule (video)
- Sum and Difference Rule (video)
- Derivative of Sine and Cosine Functions
Lesson- Rates of Change
- Position Function
- Velocity Function
- Acceleration Function
Exit Ticket
- Posted on the board at the end of the block
| Lesson Objectives
- How are the derivatives of products and quotients calculated?
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 |
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