Posted by kchik on Thursday, November 22, 2012 at 5:58am.
f = 2/3 x^3 + 3/2 x^2 - 2x + 5
f' = 2x^2 + 3x - 2
f'' = 4x + 3
f has min/max at f'=0, or x= -2 or 1/2
f''(-2) < 0 so f has a maximum there
f''(1/2) > 0 so f has a minimum there
From what you know about the general shape of cubics, this should make sense.
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