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Prove that there is a number that is exactly one more than its cube. (don’t solve just show there is one)

Prove that the function f(x)= cosx-x has a zero in (o. pi/2) Justify.

  • calculus -

    x = x^3 + 1
    x^3 - x + 1 = 0

    let f(x) = x^3 - x + 1

    every cubic function, just like every odd exponent equation, crosses the x-axis at least once.

    BTW, how about x = appr. -1.3247

    for cosx - x = 0
    cosx = x

    graph y = cosx an y = x on the same graph
    they only cross once, hence one solution

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