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Math Help - function help

  1. #1
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    Question algebra and trigonometry with analytic geometry problem

    The table shows several value of the function f(x)=-x^3+x^2-x+2. Complete the missing values in his table, and then use these values and the intermediate value theorem to determine (an) interval(s) where the function must have a zero.

    table
    x -2 -1 0 1 2
    f(x) 16 -4
    My answer is (-infty,0) u (2,infty), but I think that I'm wrong. thanks for any help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kwtolley
    The table shows several value of the function f(x)=-x^3+x^2-x+2. Complete the missing values in his table, and then use these values and the intermediate value theorem to determine (an) interval(s) where the function must have a zero.

    table
    x -2 -1 0 1 2
    f(x) 16 -4
    My answer is (-infty,0) u (2,infty), but I think that I'm wrong. thanks for any help.
    Fill in the table:

    <br />
 \begin{array}{c|ccccc}<br />
{x}& {-2}&{-1}&{0}&{1}&{2}\\<br />
{f(x)}& {16}&{5}&{2}&{1}&{-4}<br />
\end{array}<br />

    Now as x \to -\infty,\ f(x) \to +\infty, and x \to +\infty,\ f(x) \to -\infty, we have no evidence for a zero for x<-2, or x>2.

    Now f(x) changes sign in (1,2). Hence we conclude from the intermediate value theorem (and the continuity of f(x)) that f(x) has a root in this interval.

    RonL
    Last edited by CaptainBlack; June 25th 2006 at 06:42 AM.
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  3. #3
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    table messed up on me sorry

    redo of the table

    x -2 -1 0 1 2
    f(x) 16 _ _ _ -4
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