calculus I
posted by yedid on .
hi! can someone please help me ... question: a)find the intervals on which f is increasing or decreasing b)find the local max and min values of f c)find the intervals of concavity and the inflection points f(x)=2x^3+3x^26x+1 i know its a long problem but i really need help

So first of all
y' = 6x^2 + 6x  6
y'' = 12x + 6
for local max/min y'=0
6x^2 + 6x  6 = 0
x^2 + x  1 = 0
x = (1 ± √5)/2
sub that into the function to get the max/min, you do the arithmetic.
for pts of inflection, 12x+6=0
x=1/2
sub that back into the function to get the point of inflection. You do the arithm.
for concave up y'' > 0, for down y'' < 0
for 12x+6 > 0 concave up, or x > 1/2 concave up
for 12x+6< 0 concave down, or x < 1/2 concave down.