Reviewed derivative concepts by doing a Google Classroom assignment involving AP multiple choice questions.
Homework
finish the Classroom assignment
Tuesday
Warm up was 4 more AP multiple choice problems on derivatives. Started related rates lesson, learned about DREDS procedure and did several examples.
Notes from board
Homework
due Thursday: #1-11 on this handout
due Monday: p 153 #15-18, 21
Resources
look at December's posts for extrema resources for #1-11
area of a circle problem link
volume of a sphere problem, dr/dt known link
volume of a sphere problem, dV/dt known link
volume of a cube, sides expanding link
Learned about how to take derivatives of inverse functions. The formula is based on an application of the chain rule and that f(g(x))=x when f and g are inverse functions.
Notes from DS
Resources
simple inverse example: link
good inverse example: link
Thursday
Shared hw answers, then continued related rates including a cube problem and one with a cone requiring similar triangles. Introduced optimization, which involves identifying a constraint and a function to optimize, then finding the max/min of the optimization function using calculus. Worked through the fence problem as well as a few other examples (more are completed in the notes below).
Notes from board
Homework
p.153 #15-18, 21
p. 220 #17-20, 25
first test is Tuesday
Resources
see Tuesday's post above for related rates resources
box problem: link
window problem: link
maximizing rectangle in curve: link