Went over schedule for rest of the semester. Here it is:
Homework: due Weds
p. 167 #17-26 (D-AD7, D-AD8)
also see calcchat.com for help
Resources
EVT intuition: link
similar to hw: link
very similar to hw: link
Went over homework solutions in DS. Introduced Mean Value Theorem by considering average rate of change of Mr Frumble as he drove his car and noticed that a differentiable curve must at some point take on its average rate at some instant. Will cover this more on Friday. (D-CD8) Here's a video that is kind of like what we did in class (link)
Discussed increasing and decreasing behavior of functions graphically and algebraically. Noticed that a function is increasing when its derivative is positive, and a function is decreasing when its derivative is negative. Noticed that relative maxima occur at critical numbers where the slope changes from positive to negative; relative minima at those critical numbers where slope changes from negative to positive. Developed number line method (called The First Derivative Test) to classify extrema, and wrote them out to justify responses. Introduced concavity and inflection points and their relation to the second derivative. A function is concave up when its second derivative positive; f is concave down when f'' is negative. Points where a function changes concavity are known as inflection points. (D-AD7, 8, 9, 10, 11) Lecture Notes from afternoon; MVT lecture notes will be posted Friday
Homework:
Finish practice assessment
Solutions here
Resources
increasing and decreasing intervals from graph of derivative (D-AD 7 #1) link
absolute extrema (D-AD8 like #2 on practice) see Monday's post for help
using the first derivative test and number lines (D-AD8 similar to #3 on practice) link
finding increasing and decreasing intervals analytically (D-AD9, similar to #4) link
concavity intuition: stuff we covered near end of class: link
concavity of function from graph of first derivative (D-AD10, similar to #5) link
find inflection points and justify algebraically (D-AD11, similar to #6) link
Worked on practice assessment in DS. Handed out practice derivative midterms. Clean copy here. Worked through it during review session in the afternoon. Lecture board notes PDF linked here. Video of review session embedded below. Non-youtube link if needed; link
Went over assessment; took assessment. Worked through parallel lines and a geometric interpetation of the mean value theorem. Introduced concept of terrace points, inflection points, and finding concavity analytically. Also talked about the four types of curvature, illustrated with pictures.
Video examples made by Mr M to supplement notes:
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Homework
p. 192 #15-24 (D-AD10. 11)
Test on derivative rules, etc. on Monday
Resources
see above!
finding inflection points: link
mean value theorem finding c: link