![]() ![]() * Oral Review: Discussion about using the Calculator to experiment and produce a table of values to examine a function and estimate a limit as x approaches a point and as x grows without bound. ![]() Discussion about the limitation of a graphing calculator to show discontinuities in functions and the value of using a calculator to support conclusions found analytically. * Quiz – Definition and computation of derivatives * Basic differentiation rules and rates of change * The derivative and the tangent line problem * Modeling rates of change and solving related rates problems * Equations involving derivatives and problems using their verbal descriptions * Chain rule and implicit differentiation * Approximate rate of change from graphs and tables of values * Instantaneous rate of change as the limit of average rate of change * Derivative interpreted as instantaneous rate of change * Basic rules for the derivatives of sums, products, and quotients of functions * Knowledge of derivatives of power and trigonometric functions * Graphic, numeric and analytic interpretations of the derivative * Derivative defined as the limit of the difference quotient * Test – Limits and Continuity Module 2: Differentiation Suggested Pace: 5 weeks * Elluminate Session: Discussion about conditions of continuity. * Oral Review: Discussion about using a calculator to find the value of a derivative at a point, and how to graph the derived function using a calculator. ![]() Major Assignments and Assessments * Problem sets * Concavity and the second derivative test * Rolle’s Theorem and the Mean Value Theorem * Optimization – absolute and relative extrema * Analysis of curves including monotonicity and concavity * Mean Value Theorem and geometric consequences * Points of inflection as places where concavity changes * Relationship between the concavity of f and the sign of f’ * Corresponding characteristics of graphs of f, f’, and f’’ * Relationship between the increasing and decreasing behavior of f and the sign of f’ * Corresponding characteristics of graphs of f and f’ * Test – Differentiation Module 3: Applications of Differentiation Suggested Pace: 6 weeks Discussion about the limitations of the calculator to find the numerical derivative (for example, f ‘(0) for f (x) = |x|). * Oral Review: Discussion about using the calculator to find the critical values of a function by examining the graph of the function and the graph of the function’s derivative. * Find antiderivatives including the use of substitution * Use of the Fundamental Theorem of Calculus to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined * Use of the Fundamental Theorem of Calculus to evaluate definite integrals * Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: * Definite integral as a limit of Riemann sums Module 4: Integration Suggested Pace: 4 weeks
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |