- Group F: Use functions and other pre-Calculus mathematics proficiently.
- F.1: I can find the average rate of change of a function on an interval.
- Group L: Calculate, use, and explain the concept of limits.
- L.1: (CORE) I can find the limit of a function at a point using numerical, graphical, and algebraic methods.
- L.2: I can identify limits in indeterminate form and apply L'Hopital's Rule to evaluate them.
- Group D: Explain and interpret the meaning of the derivative of a function.
- D.1 (CORE): I can find the derivative of a function, both at a point and as a function, using the definition of the derivative.
- D.2 (CORE): I can use derivative notation correctly, state the units of a derivative, estimate the value of a derivative using difference quotients, and correctly interpret the meaning of a derivative in context.
- D.3 (CORE): Given information about
$f$ ,$f'$ , or$f''$ , I can correctly give information about$f$ ,$f'$ , or$f''$ and the increasing/decreasing behavior and concavity of$f$ (and vice versa). - D.4: I can determine where a function is continuous or differentiable given a graph or formula of the function and explain my reasoning.
- D.5: I can find the equation of the tangent line to a function at a point and use the tangent line to estimate values of the function.
- Group DC: Use shortcuts to calculate derivatives efficiently.
- DC.1 (CORE): I can compute derivatives correctly for power, polynomial, and exponential functions and the sine and cosine functions, and basic combinations of these (constant multiples, sums, differences).
- DC.2 (CORE): I can compute derivatives correctly for products, quotients, and composites of functions.
- DC.3: I can compute derivatives correctly using multiple rules in combination.
- DC.4: I can compute the derivatives correctly for logarithmic, trigonometric, and inverse trigonometric functions.
- Group DA: Use derivatives to solve authentic real-life application problems.
- DA.1 (CORE): I can find the critical values of a function, determine where the function is increasing and decreasing, and apply the First and Second Derivative Tests to classify the critical points as local extrema.
- DA.2: I can determine the intervals of concavity of a function and find all of its points of inflection.
- DA.3: I can use the Extreme Value Theorem to find the absolute maximum and minimum values of a continuous function on a closed interval.
- DA.4 (CORE): I can set up and use derivatives to solve applied optimization problems.
- DA.5: I can compute the derivative of an implicitly-defined function and find the slope of the tangent line to an implicit curve.
- DA.6: I can set up and use derivatives to solve related rates problems.
- Group INT: Use definite integrals and the Fundamental Theorem of Calculus to find areas and total change.
- INT.1: I can calculate the area between curves, net change, and displacement using geometric formulas and Riemann sums.
- INT.2: I can explain the meaning of each part of the definition of the definite integral in terms of a graph, and interpret the definite integral in terms of areas, net change, and displacement.
- INT.3: I can evaluate a definite integral using geometric formulas and the Properties of the Definite Integral.
- INT.4 (CORE): I can evaluate a definite integral using the Fundamental Theorem of Calculus.
- INT.5 (CORE): I can correctly antidifferentiate basic functions and identify antiderivatives.
- INT.6: I can find the average value of a function and the net change in a function over an interval using a definite integral.
Created
July 9, 2020 13:57
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