Dec.10th 2008

Well, in the beginning Mr.K talked about the project that is due on next Friday.
We looked at this graph again:

Mean Value theorem doesn't tells the value, but it tells where the value exists.
We went deeper to discuss what is the Mean Value Theorem.

Mean Value Theorem. Let f be a function which is differentiable on the closed interval [a, b]. Then there exists a point c in (a, b) such that




h'=f'-g' because h=f-gCorollary.

• Let f be a differentiable function which is positive on the closed interval [a, b]. Then f is increasing on [a, b].
• Let f be a differentiable function which is negative on the closed interval [a, b]. Then f is decreasing on [a, b].

The mean value theorem led us to the Rolle's theorem

Rolle's Theorem. Let f be a function which is differentiable on the closed interval [a, b]. If f(a) = f(b) then there exists a point c in (a, b) such that f '(c) = 0.


Rolle's Theorem and Mean Value Theorem is similar. but also different. Rolle's theorem starts and ends st the same spot, but Mean value theorem is not.

We did a problem about the Mean Value Theorem.

EX)



From Mr.K's work step by step.
1:use the formula to solve the slop of the secant line
2:find the derivative of the function.
3:plug the slop into the derivative function.
Therefore the answer is X=1

Home work for to night is
Exercises 5.5 # odds and 12


next scribe is Rence

^_^