MTH 201 Fall 2020 Learning Targets
- I can find the average rate of change of a function on an interval.
- (CORE) I can find the limit of a function at a point using numerical, graphical, and algebraic methods.
- (CORE) I can find the derivative of a function, both at a point and as a function, using the definition of the derivative.
- (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.
(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).
- I can determine where a function is continuous or differentiable given a graph or formula of the function and explain my reasoning.
- 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.
- I can identify limits in indeterminate form and apply L'Hopital's Rule to evaluate them.
- (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).
- (CORE) I can compute derivatives correctly for products, quotients, and composites of functions.
- I can compute derivatives correctly using multiple rules in combination.
- I can compute the derivatives correctly for logarithmic, trigonometric, and inverse trigonometric functions.
- (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.
- I can determine the intervals of concavity of a function and find all of its points of inflection.
- I can use the Extreme Value Theorem to find the absolute maximum and minimum values of a continuous function on a close interval.
- (CORE) I can set up and use derivatives to solve applied optimization problems.
- I can compute the derivative of an implicitly-defined function and find the slope of the tangent line to an implicit curve.
- I can set up and use derivatives to solve related rates problems.
- I can calculate the area between curves, net change, and displacement using geometric formulas and Riemann sums.
- 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.
- I can evaluate a definite integral using geometric formulas and the Properties of the Definite Integral.
- (CORE) I can evaluate a definite integral using the Fundamental Theorem of Calculus.
- (CORE) I can correctly antidifferentiate basic functions and identify antiderivatives.
- I can find the average value of a function and the net change in a function over an interval using a definite integral.