Question

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^2-6x+1 i know its a long problem but i really need help

Answer 1

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.