009A Sample Midterm 2, Problem 2 Detailed Solution
The function is a polynomial and therefore continuous everywhere.
(a) State the Intermediate Value Theorem.
(b) Use the Intermediate Value Theorem to show that has a zero in the interval
|What is a zero of the function|
|A zero is a value such that|
|Intermediate Value Theorem|
|If is continuous on a closed interval|
|and is any number between and|
then there is at least one number in the closed interval such that
|First, is continuous on the interval since is continuous everywhere.|
|Since is between and|
|the Intermediate Value Theorem tells us that there is at least one number|
|This means that has a zero in the interval|
|(a) See solution above.|
|(b) See solution above.|