Class was cut short due to report cards. Briefly went over homework on related rates, will do more discussion on this topic in Thursday DS (no open lunch that day please). Learned about optimization by first discussion in small groups how to find the maximum and minimum of a function as it relates to using the derivative. Worked through the classic problem of limited fencing enclosing a maximum area. Here is the next problem we would have worked through: direct link
Homework
p. 220 #17-21
come to DS on Thursday
first assessment is on Friday
Resources
fence problem link
box problem: link
minimum area: link
maximum volume: link
Sub was present. Lesson was self-guided based on the following notes from the board
Homework
p. 251 #7-26, 50
Practice assessment on Related Rates: Blank CORRECTED SOLUTIONS
Resources:
be sure you read through notes above :)
rationale behind reverse power rule: link
many great integral examples!!! link
Warm up on related rates dealing with a cube. Related rates assessment was a take home. Thought carefully about what it means to take an antiderivative and how it involved looking for a familiar derivative rule in the integrand, sometimes by rewriting. Did a few chain rule derivative problems and noticed that the inside part's derivative is located on the outside in some form.
This led to the idea of the reverse chain rule which involves 'cheating' by rewriting the outside part so that it looks the way we want it to (that is, so that it resembles the derivative of the inside part) but the cheat is allowed because we undo the operation on the outside of the integral. This allows us to ignore the outside part and focus on the antiderivative of the remaining function.
Notes from board
Homework
p301 #7-13
Resources
reverse chain rule concept video example video
some more examples (made by meee!) link