Pretty lost on this problem! Help needed!
Q: Suppose that 3 less than or equal to f^(x) is less than or equal to 5 for all values of x?
Show that 18 is less than or equal to f(8)- f(2) is less than or equal to 30.

- anonymous

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- schrodinger

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- anonymous

I dont really know where to start..

- dan815

Show that 18 is less than or equal to f(8)- f(2) is less than or equal to 30. what is thsi part saying

- anonymous

Here lemme right it out: Suppose that \[3\le f'x \le 5 \]

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## More answers

- dan815

oh xD thats a derivative haha

- anonymous

and show that \[18 \le f(8) - f(12) \le 30 \]

- dan815

okk

- anonymous

lol yea

- dan815

basically, lets consider the max slope and min slope

- dan815

f'(x) has a min of 3 and max of 5 slope, what can we say about the distance change from f(8) to f(12) then

- dan815

i see you wrote f(2) up in your question then f(12) rewritten which one is it exactly?

- anonymous

its f(2), sorry about that

- dan815

okay so

- dan815

do you have any ideas so far?

- anonymous

how would you solve for what f(8) and f(2) is if they dont even give you what the orignal function is?

- dan815

we dont know f(8) and f(2) but we can see the max and min difference

- dan815

|dw:1437625240205:dw|

- dan815

lets the slope function is some arbitrary function like this that si contained in slope 3 to 5

- dan815

you can say the max change will be if its slope 5 everywhere
and hte min change will be if the slope is 3 everywhere

- anonymous

yea thats given from the first info

- dan815

so you see f(8)-f(2) if f'(X) WAS 5 EVERYWHERE
and then f(8)-f(2) if f'(x) was 3 everywhere

- dan815

does this make sense?

- anonymous

yea, thanks for capitalizing it

- dan815

lol

- dan815

does it really make sense?

- anonymous

NO. I dont even get what this question is asking honestly... im super confused.

- dan815

ok ok lets start over

- anonymous

I need to go back to square 1 or something

- dan815

dont worry

- dan815

okay f'(x) the first derivatve of x means its giving u the slope of your function everywhere

- anonymous

yes, I get that

- dan815

okay now, they tell you the slope isalways somewhere in between 3 and 5

- anonymous

Yes, so we assumed 3 is the min slope and 5 is the max slope

- dan815

now our job is to find the most change possible and the least change possible for our function f(x) given this info

- dan815

we can say the most change happens when the slope is always at 5 and the least change when the slope is always at 3

- dan815

now a constnat slope means the function is a line
so to find the max and min changes we have to look at lines here

- dan815

|dw:1437625618806:dw|

- dan815

i dont know what f(8) and f(2) are but since the slope is constant i do know the changge in height

- anonymous

love the drawing, its makes more sense to me that way

- dan815

|dw:1437625668687:dw|

- dan815

|dw:1437625704207:dw|

- anonymous

wait, how were you able to assume that you could draw the right triangles like that in the diagram?

- dan815

that just me finding the change of height for a line with slope 5

- dan815

since its f(8)-f(2)
the change in x was 8-2
and to find the change in y
i know the slope of the line is 5, and slope = rise/run
so 5 slope means for every run there is 5 rise
so 8-2=6 rrun
so for 6 run there is 6*5 rise

- dan815

and the reason its right angle triangle is because run is horizontal and rise is vertical
horizontal and vertical lines have a 90 degree angle

- anonymous

OMG that was so easy!!!!

- dan815

lol xD

- dan815

im glad u find htis easy now

- anonymous

. Oops

- anonymous

Meant to say thanks! Appreciate the help! :)

- dan815

no its good,. its supposed tofeel easy once your understand it

- dan815

you already thanked me by saying omg its so easy

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