No class meeting because of weather/senior retreat?
Suggested video to prepare for derivatives (up to 10:25 mark) : link
Graph that accompanies video: link
Passed back assessments in DS then had mini-lesson on finding the value of c guaranteed to exist by the IVT for continuous functions. Did AP level multiple choice practice related to the IVT and used voting eggs to share our answers with the class. Checked over limit AP packet answers using a google form.
Began talking about the derivative with a story graph, one relating time to position. Saw that the average rate of change (slope between start and ending point) didn't accurately capture all the nuance in the graph, showing the meaning and importance of an instantaneous rate of change at individual moments in the graph. Looked at slope formula and made it look more "fancy" with notation (into something called the difference quotient) and then took the limit as the change in x approached 0. This graphically was the slope of a secant line between two points gradually becoming the slope of the tangent line at only one point. Looked at 2 different notation methods for derivatives.
Notes from board
IVT AP practice problems
Homework
None -_-
Resources
Suggested video to prepare for derivatives (up to 10:25 mark) : link
Graph that accompanies video: link
Class time was shortened due to field trip. Looked at limit definition of derivative again and worked through one example of using it and algebra to find the slope of the line tangent to a parabola at a specific point. Observed some patterns in the terms of the quadratic equation and the terms of the derivative which led to the observation of the power rule, which we looked at geometrically (we watched from 1;40 to 7:36 of this video to show the pattern geometrically). This led to the formalization of the power rule, which we then used to take the derivative of a polynomial function that would have been a big pain to do using limits and algebra. Saw that this can also be used to take derivatives of otherwise scary looking functions involving quotients and radicals by rewriting using negative and/or fractional exponents.
Notes from board
Homework
due Weds: p. 114 #5-18, 25-35 (don't forget your friend calcchat.com)
Resources
limit definition of derivative, the long and hard and ugly way: link0 (made by me!) link1 link 2
using the power rule, simple examples: link
using the power rule, having to rewrite functions first: link (made by me!)