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anonymous
 one year ago
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
 one year ago
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.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont really know where to start..

dan815
 one year ago
Best ResponseYou've already chosen the best response.1Show 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
 one year ago
Best ResponseYou've already chosen the best response.0Here lemme right it out: Suppose that \[3\le f'x \le 5 \]

dan815
 one year ago
Best ResponseYou've already chosen the best response.1oh xD thats a derivative haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and show that \[18 \le f(8)  f(12) \le 30 \]

dan815
 one year ago
Best ResponseYou've already chosen the best response.1basically, lets consider the max slope and min slope

dan815
 one year ago
Best ResponseYou've already chosen the best response.1f'(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
 one year ago
Best ResponseYou've already chosen the best response.1i see you wrote f(2) up in your question then f(12) rewritten which one is it exactly?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its f(2), sorry about that

dan815
 one year ago
Best ResponseYou've already chosen the best response.1do you have any ideas so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would you solve for what f(8) and f(2) is if they dont even give you what the orignal function is?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we dont know f(8) and f(2) but we can see the max and min difference

dan815
 one year ago
Best ResponseYou've already chosen the best response.1lets the slope function is some arbitrary function like this that si contained in slope 3 to 5

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you 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
 one year ago
Best ResponseYou've already chosen the best response.0yea thats given from the first info

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so you see f(8)f(2) if f'(X) WAS 5 EVERYWHERE and then f(8)f(2) if f'(x) was 3 everywhere

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea, thanks for capitalizing it

dan815
 one year ago
Best ResponseYou've already chosen the best response.1does it really make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0NO. I dont even get what this question is asking honestly... im super confused.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need to go back to square 1 or something

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay f'(x) the first derivatve of x means its giving u the slope of your function everywhere

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay now, they tell you the slope isalways somewhere in between 3 and 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, so we assumed 3 is the min slope and 5 is the max slope

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now our job is to find the most change possible and the least change possible for our function f(x) given this info

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we 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
 one year ago
Best ResponseYou've already chosen the best response.1now 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
 one year ago
Best ResponseYou've already chosen the best response.1i dont know what f(8) and f(2) are but since the slope is constant i do know the changge in height

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0love the drawing, its makes more sense to me that way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait, how were you able to assume that you could draw the right triangles like that in the diagram?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1that just me finding the change of height for a line with slope 5

dan815
 one year ago
Best ResponseYou've already chosen the best response.1since its f(8)f(2) the change in x was 82 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 82=6 rrun so for 6 run there is 6*5 rise

dan815
 one year ago
Best ResponseYou've already chosen the best response.1and 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
 one year ago
Best ResponseYou've already chosen the best response.0OMG that was so easy!!!!

dan815
 one year ago
Best ResponseYou've already chosen the best response.1im glad u find htis easy now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Meant to say thanks! Appreciate the help! :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.1no its good,. its supposed tofeel easy once your understand it

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you already thanked me by saying omg its so easy
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