Passed back assessments, then learned about concavity and how concave up and down behavior maps to changes in f-prime...which is to say, the value of the second derivative. Looked at the s-curve to identify an inflection point as a change in concavity. Analyzed a graph of f-prime to study its increasing/decreasing regions (as opposed to positive/ negative values) to trace the concavity of f. Found inflection points algebraically.
Notes from board
Homework
- p. 192 #15-24
- last q2 assessment is Friday (will has D-AD789 but not D-CD8, plus new concavity skills)
- finish the 11 AP questions on extrema from last Wed.
Resources
finding concavity from a graph of f-prime link
finding inflection points from a graph of f-prime: link
finding inflection points and intervals of concavity link 1 link2
finding inflection points algebraically, noting that there's no sign change: link
using both derivatives to determine inc/dec and concave up/down: link
Turned in answers to AP practice problems on extrema. Talked about concavity and how it connects with the values of the second derivative, or the inc/dec nature of the first derivative. Reviewed inflection points and saw how the concept of concavity is present in news and analysis all the time. Looked at how to 'read' a derivative graph, reviewing concepts of inc/dec and max/min and then extending to finding regions of concave up/down and locations of inflection points. Then saw how to find which of the 4 types of curvature a function exhibits by combining a sign chart for f-prime and f-double prime.
Notes from board
Homework
do the practice test, then check solutions [blank copy] [SOLUTIONS]
assessing Friday. Can do retakes in class Monday + after school Monday
Resources
see Monday's post above for resources on D-AD10 thru 13
using a graph of f-prime to determine intervals of inc/dec and relative ex LINK
finding absolute extrema on an interval: link
finding and classifying relative extrema: basic example detailed look
algebraically finding intervals of increase/decrease: link