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**Bell Ringer**
**Review**
**Lesson**
**Exit Ticket**
| **Lesson Objective(s)**
**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** |