Hi everyone! HAPPY THANKS GIVING DAY!!! It's * Katrin* and I will be your scriber yet again... =

**]**

**Today, Mr. K started off with a "The Scribe Post Hall of Fame**

**" debate, sort of thing. He asked the class, "What is a reasonable amount of votes for a peron's scribe to be inducted into the Hall of Fame?" People in the class had a lot of great ideas and I thought it was neat that that session was recorded. In the end, our class unanomously decided that**

*at least*5 votes must be made in order for a person's scribe to be in the Hall of Fame.

__In order to be inducted in the Hall of Fame__:*

**Must have at least 5 votes.***

**Conditions:****1)**

**Of the 5 votes, the**

*majority*of votes must be made by students, the rest can be external votes (Mr. K, teachers, people from all over the world, etc.).**2)**

**When voting, person must say**

*WHY*a certain person's scribe is Hall of Fame worthy.**3)**

**You**

*cannot*vote for someone just because your their friend, you have to have a reason.**------------------------------------------------------------------------------------------------**

__Daily Questions ---> Lesson:____The Derivative Function__:**1) If the average rate of change of a function f from x=1 to x=9 is known to be 3, and if f(1)=5 , find the value f(9).**

__WORK__:**Like always use the slope formula -------------->**

**Then plug it in like such:**

__Remember__:**~ f(x) = 3**

**...x**

~

**f(1) = 5**

**-----------------------------------------------------------------------------------------------****2) g(x) = x ^{2 }+ 5x**

**Find the average rate of change of**

*g*from x=a to x=a+h by calculations and simplifying:**lim.....**

__g(a+h) - g(a)__<--- numerator

h->0......(a+h) - a

h->0......(a+h) - a

**<--- denominator**

__EXAMPLE GRAPH Mr. K drew on board__:**.**

**.**

__WORK__:**Note:**

**1)*x = a***

**2) g(x) = x ^{2} + 5 x OR g(a) = a^{ 2} + 5a**

**-plug in"a" in the function, g(x) = x ^{2} + 5 x **

.

.

.

.**3)*since x=a+h then we can say that a=a+h since x=a*****-plug in (a+h) in to where you see "a" in the fuction g(a) = a ^{ 2} + 5a**

__NOTE__:

***The equation, g(a+h), in the box applies to a portion of the numerator in the equation,**

**lim..... g(a+h) - g(a) **

**h->0......(a+h) - a**

**The rest of the numerator, g(a), which equals to a**

^{2}+ 5a has its work shown below in step #5..*.***4)** **Denominator: (a+h) -a** __NOTE__:***"a" cancels out.****.**

.

5) Now we just do a matter of substitution in the equation given below and then we do some cancelling out.**lim..... g(a+h) - g(a) <--- numerator **

**h->0......(a+h) - a <--- denominator**

**Sorry if this is too small or if it appears blurry !**

**-We don't need lim h-> 0 & h anymore since its a value/number that's really really close to zero... so technically we don't need it anymore.**

__GRAPH of function g(x)=x__^{2}+ 5x and

__the derivative of that fuction:__

__g'(x)=2x+5__:**.**

**.**

**We ran out of time in the end to finish the last question. Mr. K said he would post the answers up for that.**

__HOMEWORK__: 2.3 odd #'s & # 12**The person I choose to do the next scribe is**

*Ashlynn*! :)
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