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Thread: Continuous Functions

  1. #1
    Senior Member
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    Continuous Functions

    I'm having trouble with this question. I think we have to use the intermediate value theorem for this question.

    $\displaystyle Show\ that\ f(x)=x^3-5x+3$ $\displaystyle has\ a\ zero\ in\ each$ $\displaystyle of\ the\ intervals\ [-3,-2],\ [0,1]\ and\ [1,2].$
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  2. #2
    MHF Contributor

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    Use the "intermediate value property"- if f is a continuous function and f(a)< f(b), then, for x between a and b, f(x) takes on every value between f(a) and f(b).

    For example, $\displaystyle f(-3)= (-3)^3- 5(-3)+ 3= -27+ 15+ 3= -9< 0$ while $\displaystyle f(-2)= (-2)^3- 5(-2)+ 3= -8+ 10+ 3= 5> 0$.
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