Lecture 16:

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Assignment

For today you should have completed the problems 15-21, 53, 55 in section 3.1 and problems 23, 25, 31-33, 37 and 41 of section 3.2. Problems 9, 21, 31, 36, 49, and 55 of section 3.5 are due on Friday, Febuary 20 as well.

REMEMBER -- EXAM #2 IS ON February 27 !!!

Brief review of the lecture

The Intermediate Value Theorem states that every function which is continuous over an interval of numbers has the intermediate value property over that interval. The intermediate value property over the interval [a,b] states the following: if the number M is caught between f(a) and f(b), then there is a number c in the interval [a,b] such that f(c)=M.

This useful theorem is important in isolating the roots of a polynomial and of other continuous functions. If we find that for polynomial p, p(a) is negative and p(b) is positive, then the theorem states that p has a root between a and b.

The next topic is differentiation. We discussed and showed examples of the use of the four step process for calculating a derivative. It is important to practice this process.

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