K–12 teaching and learning · from the UNC School of Education
- Classroom
- Professional
- My LEARN NC
- Objective 2.01
- Explore and interpret the concept of the derivative graphically, numerically, analytically and verbally.
- Interpret derivative as an instantaneous rate of change.
- Define derivative as the limit of the difference quotient.
- Identify the relationship between differentiability and continuity.
- Find related resources
- Objective 2.02
- Apply the concept of the derivative at a point.
- Find the slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents.
- Find the tangent line to a curve at a point and local linear approximation.
- Find the instantaneous rate of change as the limit of average rate of change.
- Approximate a rate of change from graphs and tables of values.
- Find related resources
- Objective 2.03
- Interpret the derivative as a function.
- Identify corresponding characteristics of graphs of ƒ and ƒ'.
- Identify relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ'.
- Investigate the Mean Value Theorem and its geometric consequences.
- Translate between verbal and algebraic descriptions of equations involving derivatives.
- Find related resources
- Objective 2.04
- Demonstrate fluency and accuracy in the computation of derivatives.
- Find the derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
- Use the basic rules for the derivative of sums, products, and quotients of functions.
- Use the chain rule and implicit differentiation.
- Find related resources
- Objective 2.05
- Interpret the second derivative.
- Identify the corresponding characteristics of the graphs of ƒ, ƒ', and ƒ".
- Identify the relationship between the concavity of ƒ and the sign of ƒ".
- Identify points of inflection as places where concavity changes.
- Find related resources
- Objective 2.06
- Apply the derivative in graphing and modeling contexts.
- Analyze curves, with attention to monotonicity and concavity.
- Optimize with both absolute (global) and relative (local) extrema.
- Model rates of change, including related rates problems.
- Use implicit differentiation to find the derivative of an inverse function.
- Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.
- Interpret differential equations geometrically via slope fields and the relationship between slope fields and solution curves for differential equations.
- Find related resources
