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I dont really know where to start..

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

oh xD thats a derivative haha

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

okk

lol yea

basically, lets consider the max slope and min slope

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

its f(2), sorry about that

okay so

do you have any ideas so far?

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

|dw:1437625240205:dw|

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

yea thats given from the first info

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

does this make sense?

yea, thanks for capitalizing it

lol

does it really make sense?

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

ok ok lets start over

I need to go back to square 1 or something

dont worry

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

yes, I get that

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

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

|dw:1437625618806:dw|

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

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

|dw:1437625668687:dw|

|dw:1437625704207:dw|

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

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

OMG that was so easy!!!!

lol xD

im glad u find htis easy now

. Oops

Meant to say thanks! Appreciate the help! :)

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

you already thanked me by saying omg its so easy