__Monday__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

__Wednesday__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

__Friday__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