Information:
Given defined by
The problem:
Find a so that implicates that for all and in
I was told that the mean value theorem can be used to find our . Don't know how though. Any ideas on how to proceed?
This is what I did. Please correct any mistakes:
Given defined by .
We want to find a so that implicates that for all and in
The mean value theorem says that since f is countinous for , we have:
where
By graphing we see that this (absolute) value is never greater than 4 (or 5, or 6...). We now have that:
Let's say that , where we have been told that . Since , then .
So finally:
Therefore is a value for that makes