Here is the packet (Due Jan 4)
Here are some helpful hints: LINK [#13 worked out, remember to skip #7 for now]
Applications of Derivatives!
Here is the packet (Due Jan 4) Here are some helpful hints: LINK [#13 worked out, remember to skip #7 for now] Monday Checked over absolute extrema homework. Went over how to identify relative extrema on a graph, which led to discussion on sign change from critical numbers. Introduced first derivative test and how to find, classify, and justify relative maxima and minima algebraically. Notes from board Homework finish practice assessment [blank] [SOLUTIONS] assessment is in class Wednesday Resources using a graph of f-prime to determine intervals of increase/decrease and relative extremes (D-AD7) LINK finding absolute extrema on an interval: link finding and classifying relative extrema: basic example detailed look [D-AD8] algebraically finding intervals of increase/decrease: link [D-AD9] mean value theorem algebraically: link [D-CD8] Position/velocity/acceleration: link [D-AD7] (made by me just for youuuu!) Wednesday Went over practice assessment in DS, took real thing in class. Also learned about concavity, difference in concave up and down and how the rate of change (slope) increases as x increases in a concave up graph, and how the rate of change decreases for concave down. This leads to the realization that f-double-prime's sign tells you the concavity of F. Where a function changes concavity is a special point called an inflection point, and it is found in a manner very similar to relative extrema, except using the second derivative instead of the first. Notes from board Homework p. 192 #15-24 [D-AD11, D-AD12] Resources forthcoming Friday
Warm up dealing with analyzing concavity given graphs and tables. Later, got a graph of F-prime and had to figure out where F was concave up and concave down. This is done by analyzing where F-prime is increasing (So F-doubleprime is positive, so F is concave up) and where F-prime is decreasing (So F-doubleprime is negative, so F is concave down). Did another algebraic example of finding intervals of concavity, this time requiring use of the quotient rule. Finally combined concavity information from the second derivative and increasing/decreasing information from the first derivative to figure out the type of curvature at a certain point and also to find intervals that were increasing or decreasing in a certain manner (concave up or down). This required the use of two simultaneous "sign charts" and careful analysis. Notes from board Homework Work on practice assessment [blank copy] [SOLUTIONS] Assessment on Monday 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 for D-AD7 thru 9, check out Monday's resources above |
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September 2018
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