This sample material is the first investigation from Lesson 2, "Rates of Change of Familiar Functions." In this investigation, students use methods of estimating instantaneous rates of change learned in Lesson 1 to estimate rates of change at specific points for linear, quadratic, exponential, and trigonometric functions. In the remainder of this lesson, students discover ways to use a function rule to find the rule of its derivative and investigate how the shape of the graph of a function can be used to describe and sketch the graph of its derivative.
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.
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In the remainder of Course 4, students develop understanding of logarithmic functions and their use in modeling and analyzing problem situations.
Students intending to pursue college majors in the mathematical, physical, and biological sciences and engineering extend their ability to use polynomial and rational functions to solve problems and extend their ability to manipulate symbolic representations of exponential, common and natural logarithmic, and trigonometric functions.
A unit that develops understanding and skill in the use of standard spreadsheet operations while reviewing and extending many of the basic algebra topics from Courses 1-3 is included for students intending to pursue college programs in social, management, and some of the health sciences or humanities.
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