anonymous
  • anonymous
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.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I dont really know where to start..
dan815
  • 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
  • anonymous
Here lemme right it out: Suppose that \[3\le f'x \le 5 \]

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dan815
  • dan815
oh xD thats a derivative haha
anonymous
  • anonymous
and show that \[18 \le f(8) - f(12) \le 30 \]
dan815
  • dan815
okk
anonymous
  • anonymous
lol yea
dan815
  • dan815
basically, lets consider the max slope and min slope
dan815
  • 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
  • dan815
i see you wrote f(2) up in your question then f(12) rewritten which one is it exactly?
anonymous
  • anonymous
its f(2), sorry about that
dan815
  • dan815
okay so
dan815
  • dan815
do you have any ideas so far?
anonymous
  • 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
  • dan815
we dont know f(8) and f(2) but we can see the max and min difference
dan815
  • dan815
|dw:1437625240205:dw|
dan815
  • dan815
lets the slope function is some arbitrary function like this that si contained in slope 3 to 5
dan815
  • 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
  • anonymous
yea thats given from the first info
dan815
  • 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
  • dan815
does this make sense?
anonymous
  • anonymous
yea, thanks for capitalizing it
dan815
  • dan815
lol
dan815
  • dan815
does it really make sense?
anonymous
  • anonymous
NO. I dont even get what this question is asking honestly... im super confused.
dan815
  • dan815
ok ok lets start over
anonymous
  • anonymous
I need to go back to square 1 or something
dan815
  • dan815
dont worry
dan815
  • dan815
okay f'(x) the first derivatve of x means its giving u the slope of your function everywhere
anonymous
  • anonymous
yes, I get that
dan815
  • dan815
okay now, they tell you the slope isalways somewhere in between 3 and 5
anonymous
  • anonymous
Yes, so we assumed 3 is the min slope and 5 is the max slope
dan815
  • 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
  • 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
  • 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
  • dan815
|dw:1437625618806:dw|
dan815
  • 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
  • anonymous
love the drawing, its makes more sense to me that way
dan815
  • dan815
|dw:1437625668687:dw|
dan815
  • dan815
|dw:1437625704207:dw|
anonymous
  • anonymous
wait, how were you able to assume that you could draw the right triangles like that in the diagram?
dan815
  • dan815
that just me finding the change of height for a line with slope 5
dan815
  • 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
  • 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
  • anonymous
OMG that was so easy!!!!
dan815
  • dan815
lol xD
dan815
  • dan815
im glad u find htis easy now
anonymous
  • anonymous
. Oops
anonymous
  • anonymous
Meant to say thanks! Appreciate the help! :)
dan815
  • dan815
no its good,. its supposed tofeel easy once your understand it
dan815
  • dan815
you already thanked me by saying omg its so easy

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