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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    First find derivative

  2. anonymous
    • 5 years ago
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    3cosx-3sinx

  3. anonymous
    • 5 years ago
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    to find inflection points, just take the second derivative, set it to zero and solve for x.

  4. anonymous
    • 5 years ago
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    so the second derivative is -3sinx-3cos x

  5. anonymous
    • 5 years ago
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    but how would i solve for that

  6. anonymous
    • 5 years ago
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    factor out the -3?

  7. anonymous
    • 5 years ago
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    set to 0 solve for x

  8. anonymous
    • 5 years ago
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    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 :)

  9. anonymous
    • 5 years ago
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    what about the concave up and down?

  10. anonymous
    • 5 years ago
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    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 :)

  11. anonymous
    • 5 years ago
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    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

  12. anonymous
    • 5 years ago
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    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 :)

  13. anonymous
    • 5 years ago
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    but since its between 0 and 2pi i do 0, pi/2, pi/3, pi?

  14. anonymous
    • 5 years ago
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    Been a while since I did this. We need Lokisan or Xavier

  15. anonymous
    • 5 years ago
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    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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