Rescheduled test to tomorrow. Studied and reviewed.
Notes from board, including additional book practice
Homework
finish practice assessment (blank copy) (SOLUTIONS)
Resources
using a graph of f-prime to determine intervals of inc/dec and relative ext LINK
finding absolute extrema on an interval: link
finding and classifying relative extrema: basic example detailed look
algebraically finding intervals of increase/decrease: link
tangent line approximations: link
implicit differentiation and finding slope at a point: link1 link2
interpreting the derivative link1 link2 link3 link4
Took (and passed! hopefully :)) the assessment
Homework
watch and take notes on these 2 videos: link1 link2
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Thursday
Passed back assessments, looked at some common mistakes. Reviewed the MVT based on the videos above, and looked into some of the conceptual basis for why its true. Basically it applies the fact that a differentiable function F means F' is continuous, which means the IVT applies to F'. Found the value of c guaranteed to exist by the MVT as well.
Reviewed curvature types, and saw that the increasing/decreasing nature of F-prime is what specifies the concavity of F. Another way to say this is that the concavity of F is related to the positive/negative values of F-doubleprime. Analyzed a first derivative graph to find increasing and decreasing intervals of F along with relative extrema (which was on the last test) and also looked for intervals of concave up and down for F and locations of inflection points for F (which is new). Basically, F is concave up where F-prime is increasing, and down where decreasing. Inflection points on F are where F-prime has relative max and mins.
Showed how to find intervals of concave up/down as well as inflection points by basically doing the same procedure we used with sign charts and such except this time, working entirely with the second derivative. Tied this together with increasing and decreasing locations to specify precisely what a function is doing in terms of the 4 kinds of curvature by analyzing the values of both F-prime and F-doubleprime simultaneously.
Notes from board
Homework
p.175 #37-42
p.192 #15-22, 53-54
remember calcchat.com
Resources
mean value theorem algebraically: link
intuition of the mvt (similar to what was discussed in class) link
additional MVT example: link
how to find the value guaranteed by the MVT: link
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