anonymous
  • anonymous
f(x) = 3 sin x + 3 cos x 0 ≤ x ≤ 2π. Find the interval in which f is concave up and concave down. Find the inflection points
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
First find derivative
anonymous
  • anonymous
3cosx-3sinx
anonymous
  • anonymous
to find inflection points, just take the second derivative, set it to zero and solve for x.

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anonymous
  • anonymous
so the second derivative is -3sinx-3cos x
anonymous
  • anonymous
but how would i solve for that
anonymous
  • anonymous
factor out the -3?
anonymous
  • anonymous
set to 0 solve for x
anonymous
  • anonymous
to find the inflection points, you have to derive your function twice, and then you'll have to take 2 conditions. 1) f''(x) = 0 2) f''(x) = UND depends on the function ofcourse when you set your derived function to zero, you'll get numbers, those are your x's and to find the y's to finish up your process , plug in the x you found in the original function, and with that, you'l have your inflection points ^_^ I hinted it for you, now give it a try :)
anonymous
  • anonymous
what about the concave up and down?
anonymous
  • anonymous
for that, you have to draw a table putting in the x, f''(x), and f in the first column like this : x | (--) 0 (+) ___|________________________ f'' | ___|_________________________ f | then you take negative values for x and plug them in the original function, if it gives you a negative answer then it's concaved down, and if it gives you a positive answer then it's concaved up. Same story goes when you take positive values for x~ after that, from the table, you'll be able to determine the intervals of concavity :)
anonymous
  • anonymous
This one is tricky. I think you have to plot sin x - cos x over your interveral 0 to 2 pi. You would get your max and min because it is a periodic function
anonymous
  • anonymous
oh, right, so you'll hav to list the x's on the x's row lol, you know -2pi -pi -pi/2 0 pi/2 ...e.tc :)
anonymous
  • anonymous
but since its between 0 and 2pi i do 0, pi/2, pi/3, pi?
anonymous
  • anonymous
Been a while since I did this. We need Lokisan or Xavier
anonymous
  • anonymous
You make a table x=0, f' (x) (or f''(x) which ever one=sinx - cos x. You evaluate over 4 intervals, you would get your max, min

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