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-g

**Corollary.**

- 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

**Let**

Rolle's Theorem.

Rolle's Theorem.

**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

^_^

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

^_^

## 1 comment:

Good Job ^__^

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