Update
Questions
Bell RingerFind the x-coordinate that has a horizontal tangent line for the following: -2 0 2 3 none of the above
Does the point in #1 occur at a maximum or a minimum on the graph? maximum minimum neither
Find the x-coordinate in which the following function does not have a derivative: 0 2 -2 1 none of the above
Does the point in #3 occur at a maximum or a minimum on the graph? maximum minimum - neither
Review
Lesson
Exit Ticket
| Lesson Objective(s)
- How is the derivative used to locate the minimum and maximum values of a function on a closed interval?
Skills
- Find critical numbers using differentiation.
- Find extrema on a closed interval using differentiation.
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 |