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I use this activity in Honors Advanced Algebra (Algebra 2). This is a Pre-AP course and students are introduced to the concepts of instantaneous rate of change, equations of tangent lines, and equations that represent the slope at any point on the curve (derivatives). The goal is for early exposure to the these concepts to increase success in Calculus.
Prior to this activity the concept of slope at a point (instantaneous rate of change) had been introduced to students. Students also had identified turning points and points of inflection through visually analyzing the graphs of various polynomial functions. They had also been introduced to the idea that at these critical points the instantaneous rate of change is zero.
The goal of this activity is to have students practice graphing (curve sketching) using their knowledge of intercepts of polynomial functions and by using the slope equation (derivative) to find the critical points in order to get a more accurate sketch.
The zip file contains an editable word document with the assignment and a pdf file with copies of the solutions.