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anonymous
 5 years ago
Find where the function is concave up: f(x) = 3x4  2x3 – 3x
anonymous
 5 years ago
Find where the function is concave up: f(x) = 3x4  2x3 – 3x

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So far I did find f '(x)which equals 12x^36x^23

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f'' is a good test for cave up....which is a MIN find your "zeros" for the f' and that will tell you what "x" values you need to use for the next part..

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03(4x^3 2x^2 1) narrows it down. 4x^3 2x^2 1 = 0 x^2(4x2) = 1 might help

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets go ahead and find the f'' might be easier

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f'' = 36x^2  12x now we can partition this out to determine what values we get for the number line

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.012x(3x 1).... we have zero values at 0 and 1/3 these are out inflections if were lucky <........0.........1/3..........>  + +   +  +  + getting warmer

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.00 and 1/3 are our inflections were the concavity changes (inf,0) = cave up (0,1/3) = cave down (1/3, inf) = cave up so this thing looks like a "W"
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