Submitted AP Limits packet answers via Google Classroom. Did another example with the limit definition of derivative and a quadratic equation. Started looking at average rate of change vs. instant rate of change and how the formed is just the slope between 2 points and the latter is a slope at a single point (aka the value of the derivative).
Notes from board
Homework
#1-4 on this handout (numerical answers here)
Resources
limit definition of derivative (first half of this vid) link
avg vs instantaneous rate of change (guy in video uses right endpoint vs left but same idea) link
Tuesday
Answered questions on limits handout at start of class, then shared HW answers. Reexamined the central problem of calculus which deals with how to 'linearize' complicated, curvy functions by mimicking their behavior with a tangent line. Did a numerical exploration together on Desmos which showed a pattern between a power function like x^3 and the values of its derivative using the limit definition (which followed the pattern of 3x^2). This led to the power rule, one of the most important in calculus. Worked a few basic examples, then saw how many things that can be differentiated using the power rule first need to be 'cleaned up for prom' by utilizing negative and/or fractional exponents and then applying the power rule. Started making our formulas booklet.
Notes from board
Homework
p. 114 #3-18, 25-30, 39-46
don't forget calcchat.com
Resources
power rule simple examples: link
how to handle rational terms: link
how to handle a simple square root
power rule for rational functions (#25-30) link [also see p 110 ex 6 at top of page]
rewriting involving nth roots and fractions: link (starts at 3:35)
power rule examples (feat me :) ) link
equation of a tangent line + graph (feat me :) link
We did more stuff with the power rule in DS. Here are the notes.
Thursday
Warm up was to apply the power rule to a 3 different functions. We did a quick check up involving taking a simple derivative (phrased as finding the slope of the tangent line) evaluated at a single point. Looked at how the calculator can be used to evaluate derivatives at a point (numerical) but not to actually produce the derivative function. (Here is how the calculator is used for this: link). Looked again at the 'cartoons' which help create a mental image for some of the calculus topics we discuss. Reviewed some terminology distinguishing derivatives as a value and derivatives as a function, as well as defining "differentation".
Reviewed the Algebra I concept of writing the equation of a line passing through 2 points and 'upgraded' this to the calculus concept of writing the equation of a tangent line. Finally, used the calculator's numerical derivative operation again to discover the derivative of sine (which is cosine). See here for an explanation.
Notes from board
Homework
#1-20 on this handout for Monday
start working on the practice assessment for Tuesday (which is when the test is)
(blank copy of practice)
(SOLUTIONS for practice)
Resources for Handout made by me :)
Use the limit definition of derivative to find a derivative (#1-4) link
power rule examples (#5- 16) link
equation of a tangent line + graph (#17-20) link
Resources for Practice Assessment
review of IVT: link1 link2
using the IVT (starts at 5:20): link
finding c by the IVT: link link2
limit definition of derivative, the long and hard and ugly way: link0 link1 link 2
using the power rule, simple examples: link
using the power rule, having to rewrite functions first: link
finding limits from a graph link
finding limits by factoring and canceling: link
bunch of worked out basic limit examples: link
find and classify discontinuities, justify with limits: link
horizontal asymptotes using limits: link
vertical asymptotes using limits: link