# analysis of polynomial function

• Sep 3rd 2010, 05:51 AM
euclid2
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?
• Sep 3rd 2010, 07:13 AM
yeKciM
Quote:

Originally Posted by euclid2
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?

you have real root \$\displaystyle x = 0,78\$ (zero of the function )

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