analysis of polynomial function

for the function $\displaystyle f(x)=x^3-x^2+4x-3$ 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?