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Math Help - Help applying the intermediate value theorem

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    Help applying the intermediate value theorem

    Show that the equation x^3=5 has a solution on the interval [1,2]
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    Quote Originally Posted by Livingg90 View Post
    Show that the equation x^3=5 has a solution on the interval [1,2]
    Consider the function

    f(x)=x^3-5 and note that

    f(1)=1^3-5=-4 and

    f(2)=2^3-5=3

    Since polynomials are continous by the intermediate value theorem there exists c \in (1,2) such that f(c)=0

    f(c)=0=c^3-5 so the equation has a solution
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