Scribe Post: Day 20 - Lesson: The Derivative Function

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.

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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

GRAPH:

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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 <--- denominator




EXAMPLE GRAPH Mr. K drew on board:














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WORK:



Note:

1)*x = a*

2) g(x) = x² + 5 x OR g(a) = a ² + 5a

-plug in"a" in the function, g(x) = x² + 5 x

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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.

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4) Denominator: (a+h) -a


NOTE:
*"a" cancels out.


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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)=x² + 5x and
the derivative of that fuction: g'(x)=2x+5:

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

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HOMEWORK: 2.3 odd #'s & # 12

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The person I choose to do the next scribe is Ashlynn! :)