MTH 201 Fall 2020 Learning Targets.md

MTH 201 Fall 2020 Learning Targets

1. I can find the average rate of change of a function on an interval.
2. (CORE) I can find the limit of a function at a point using numerical, graphical, and algebraic methods.
3. (CORE) I can find the derivative of a function, both at a point and as a function, using the definition of the derivative.
4. (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.
5. (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).
6. I can determine where a function is continuous or differentiable given a graph or formula of the function and explain my reasoning.
7. 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.
8. I can identify limits in indeterminate form and apply L'Hopital's Rule to evaluate them.
9. (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).
10. (CORE) I can compute derivatives correctly for products, quotients, and composites of functions.
11. I can compute derivatives correctly using multiple rules in combination.
12. I can compute the derivatives correctly for logarithmic, trigonometric, and inverse trigonometric functions.
13. (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.
14. I can determine the intervals of concavity of a function and find all of its points of inflection.
15. I can use the Extreme Value Theorem to find the absolute maximum and minimum values of a continuous function on a close interval.
16. (CORE) I can set up and use derivatives to solve applied optimization problems.
17. I can compute the derivative of an implicitly-defined function and find the slope of the tangent line to an implicit curve.
18. I can set up and use derivatives to solve related rates problems.
19. I can calculate the area between curves, net change, and displacement using geometric formulas and Riemann sums.
20. 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.
21. I can evaluate a definite integral using geometric formulas and the Properties of the Definite Integral.
22. (CORE) I can evaluate a definite integral using the Fundamental Theorem of Calculus.
23. (CORE) I can correctly antidifferentiate basic functions and identify antiderivatives.
24. I can find the average value of a function and the net change in a function over an interval using a definite integral.