Warm up dealt with reading a velocity graph in depth. Announced next assessment, which is on Monday 11/20. Learned about implicit differentiation which involves the chain rule and using the derivative as an operator.
Notes from board
Homework
finish the worksheet assigned Friday, due this Wednesday (skip 640 and 649)
(blank copy) (numerical answers)
Due Friday: p. 145 #3-39 (mult of 3)
Resources
basic premise of implicit differentiation: link
implicit differentiation involving product rule: link
implicit differentiation involving product rule to find slope at a point: link
deep dive into the mechanics of implicit differentiation for those curious: link
Went over the Derive/Derivado worksheet in DS and did some more implicit differentiation, involving trig. In class, did several more implicit differentiation problems, involving the product rule, finding tangent/normal lines, finding slope at a point, and even finding the second derivative implicitly. Looked briefly at how to find points where a function has horizontal or vertical tangents.
Notes from board
Homework
p. 145 #3-39 (mult of 3) ignore instructions to graph or solve explicitly
practice assessment due Monday (blank copy) (numerical answers) (SOLUTIONS)
Resources
implicit differentiation to find second derivative: LINK
another implicit second derivative: link
finding acceleration at a time given position function, using trig and chain rule (like #1): link
find when a moving object is at rest (like #2) link
how to read a velocity graph (like #3) link
using implicit differentiation to find slope given an x-value (feat me working out #4): link
implicit differentiation to find dy/dx (feat me working out #5) link
writing equation of tangent line, given the slope (feat me doing #7): link
showing differentiability (like #8) link
finding values to make a function differentiable (like #9): link
tangent line approximations (like #10 and 11) link link 2
concept behind horizontal and vertical tangents, (examples by me! helps with #12 and 13) link
Warm up dealt with using implicit differentiation to find the location of a vertical tangent. Also looked back at the limit definition of derivative to use pattern recognition to figure out how to solve an otherwise difficult problem by using derivative rules. Went over HW briefly then continued with vertical/horizontal tangents with a problem that required special factoring to re-write as a rational function. Introduced L'Hopital's Rule as a method of solving limit problems that result in an indeterminate form (like 0/0, among others--see notes) by taking the derivatives of the numerator and denominator and trying direct substitution again.
Notes from board
Homework
practice assessment (blank copy) (numerical answers) (SOLUTIONS)
real assessment is Monday
Resources
(see Wednesday's post for assessment study resources, below is L'Hopital's Rule)
basic introduction to L'Hopital's Rule: link
some examples of l'Hopital's Rule link
more good l'Hopital's Rule examples, including when not to use: link