Find where the function is concave up: f(x) = 3x4 - 2x3 – 3x

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Find where the function is concave up: f(x) = 3x4 - 2x3 – 3x

Mathematics
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So far I did find f '(x)which equals 12x^3-6x^2-3
f'' 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..
3(4x^3 -2x^2 -1) narrows it down. 4x^3 -2x^2 -1 = 0 x^2(4x-2) = 1 might help

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lets go ahead and find the f'' might be easier
f'' = 36x^2 - 12x now we can partition this out to determine what values we get for the number line
12x(3x -1).... we have zero values at 0 and 1/3 these are out inflections if were lucky <........0.........1/3..........> - + + - - + ---------------------- + - + getting warmer
0 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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