# Math Help - analysis of polynomial function

1. ## analysis of polynomial function

for the function $f(x)=x^3-x^2+4x-3$ determine:

a/ the intervals of increase of decrease
b/ the location of any max/min points
c/ the intervals of concavity up or down
d/ the location of any points of inflection

for a/ i get f'(x)=3x^2-2x+4 and i tried plugging into quadratic formula since it is unfactorable and got a negative number under the radical so does that mean there are no real roots or zeros? so how would i figure out max/min? and increase decrease?

2. Originally Posted by euclid2
for the function $f(x)=x^3-x^2+4x-3$ determine:

a/ the intervals of increase of decrease
b/ the location of any max/min points
c/ the intervals of concavity up or down
d/ the location of any points of inflection

for a/ i get f'(x)=3x^2-2x+4 and i tried plugging into quadratic formula since it is unfactorable and got a negative number under the radical so does that mean there are no real roots or zeros? so how would i figure out max/min? and increase decrease?
you have real root $x = 0,78$ (zero of the function )

and for stationary points, you should do first derivation to find if there is any stationary points , and second derivation to check concavity ... and so on