Bell Ringer
Review
- Pre-calculus
- Slope
- Equation of a Line
- Secant Line vs. Tangent Line (video)
- Tangent Line
- How can the slope of one point be found?
- Equation of a Tangent Line (video)
- Derivative (video) (checkpoints)
- How are derivatives related to tangent lines?
- Finding the derivative of polynomials using limits (example)
- Basic Differentiation Rules
- How can derivatives be calculated using basic differentiation rules?
- Product Rule/Quotient Rule (checkpoints)
- How can derivatives of the product/quotient of functions be calculated?
Lesson
Exit Ticket
- Posted on the board at the end of the block.
Homework
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Lesson Objectives
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.9
- Apply formulas to find derivatives.
- Includes:
- derivatives of algebraic,
trigonometric, exponential, logarithmic, and inverse trigonometric functions - derivations of sums, products, quotients, inverses, and composites (chain rule) of elementary functions
- derivatives of implicitly defined functions
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