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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
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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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0First find derivative

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to find inflection points, just take the second derivative, set it to zero and solve for x.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the second derivative is 3sinx3cos x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but how would i solve for that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to 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
 5 years ago
Best ResponseYou've already chosen the best response.0what about the concave up and down?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for 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
 5 years ago
Best ResponseYou've already chosen the best response.0This 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
 5 years ago
Best ResponseYou've already chosen the best response.0oh, 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
 5 years ago
Best ResponseYou've already chosen the best response.0but since its between 0 and 2pi i do 0, pi/2, pi/3, pi?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Been a while since I did this. We need Lokisan or Xavier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You 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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