LaddiusMaximus
  • LaddiusMaximus
Determine the values of x for which the function f is decreasing, where f(x)=(440−x)^(2)+x^(2) enter your answer in interval notation use your answer to determine which is bigger, 154^(2) + 286^(2) or 198^(2) + 242^(2)
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
take the derivative to get f'(x) = 2(440 - x)(-1) + 2x = -880 + 4x. Find the zeros of the derivative to get x = 220. your intervals are (-inf, 220), (220, inf). pick a value in these intervals and plug in to the derivative, if negative, f is decreasing. if positive, f is increasing.
LaddiusMaximus
  • LaddiusMaximus
find the zeros?
precal
  • precal
solve for 0 ie -880+4x=0

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precal
  • precal
Actually it was done for you 220
precal
  • precal
|dw:1333584049330:dw|
precal
  • precal
Pick a number from the intervals, and test it to see if it is positive or negative
LaddiusMaximus
  • LaddiusMaximus
i plug the number into 4x-880?
precal
  • precal
|dw:1333584259447:dw|
LaddiusMaximus
  • LaddiusMaximus
I dont understand. I apologize
LaddiusMaximus
  • LaddiusMaximus
how does this determine what is bigger or smaller?
precal
  • precal
|dw:1333584585624:dw|
precal
  • precal
no we just want to know if the numbers are positive or negative.
precal
  • precal
positive is increasing negative is decreasing ok did you figure out those two I gave you above
LaddiusMaximus
  • LaddiusMaximus
no. I dont understand what you are doing. My answer is 220. okay I got that. then what?
precal
  • precal
you draw a number line and find a number to the right and left of 220. I picked 0 and 221 so waht are their y values sub into f '(x)
LaddiusMaximus
  • LaddiusMaximus
you mean f(x)=(440-x)^(2)+x^(2)?
precal
  • precal
|dw:1333584994687:dw|
precal
  • precal
|dw:1333585016863:dw|
LaddiusMaximus
  • LaddiusMaximus
so the answer is (4,220)?
precal
  • precal
No
LaddiusMaximus
  • LaddiusMaximus
well im lost because it want the answer in interval notation\
precal
  • precal
|dw:1333585715666:dw|
LaddiusMaximus
  • LaddiusMaximus
ok what did that number line have to do with anything? and the f'(0)=-880?
precal
  • precal
Helps us determine the number of intervals that we need. 0 and 221 are numbers in the intervals positive numbers tell us that they are increasing negative numbers tell us that they are decreasing Is this for AP calculus? Because AP calculus does not accept this as the only method for a solution
LaddiusMaximus
  • LaddiusMaximus
no its just calc 1 on webworks. I put that interval in and it said it was wrong.
LaddiusMaximus
  • LaddiusMaximus
i just dont know what I am doing.
precal
  • precal
You should check out www.khanacademy.org or maybe it is .com He has alot of videos in calculus and you can log in and do practice problems.
LaddiusMaximus
  • LaddiusMaximus
ok the answer is (-inf, 220) but how do I use that to solve the next part?
precal
  • precal
I am not sure what you mean about the next part
LaddiusMaximus
  • LaddiusMaximus
it says use your answer to see which is bigger 154^(2) + 286^(2) or 198^(2) + 242^(2)

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