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Math Help - analysis of polynomial function

  1. #1
    Senior Member euclid2's Avatar
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    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?
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by euclid2 View Post
    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
    Attached Thumbnails Attached Thumbnails analysis of polynomial function-function_x3-x2-4x-3.jpg  
    Last edited by yeKciM; September 3rd 2010 at 07:24 AM.
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