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Tuesday, January 6, 2009

BOB for Chapter Five

Darn, that break really messed me up. Before the break I felt like I was on a roll with the questions in the chapter. Now that I look at the questions one last time before the test, I feel like I'm almost new to the subject. What I do remember from "Last Year" was the Mean Value Theorem, some Optimization Problems, and How to use the First and Second Derivatives.

The Mean Value Theorem says that if a function is differentiable and continuous within a closed interval, the secant line connecting the 2 endpoints of the function will have a slope equal to, at least, one other tangent line of another point on that function within the interval.

Optimization Problems are word problems involving situations where you want to have the most or least of something. Some examples include maximizing number products sold while minimizing production costs, or maximizing the area of a shape inscribed another shape with limited dimensions.

The main point of this chapter is to learn the many uses of the First and Second Derivatives.
The First Derivative can be used to find many things about the parent function, but the main use is to find the critical point(s) of the parent function that may exist and on what interval(s) is the parent function is increasing or decreasing. Critical Points include Local/Global Maxima (Max or Mins).
The main use of the Second Derivative is to find on which interval(s) is the parent function concave up or down and where the parent function has an inflection point (change in concavity).

Once I saw the word Antiderivatives again after the break, everything that we learned "Last Year" flew back into my head. *That was the coolest flashback I ever had.
To antidifferentiate a function is to find the parent function if the first derivative is given, the first derivative if the second derivative is known, etc.

Overall I think I'm going to do okay. It may take me a while to complete it though.
Good luck and see you all tomorrow.

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