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Calculus

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Use the intermediate value therom to show that there is a root of the given equation in the specified interval.

x^5-7=2(25-x); (2,3)



Please explain for understanding and show work, Thank you in advance :)

  • Calculus -

    x^5 - 7 = 50 - 2x

    x^5 + 2 x - 57 = 0

    y = x^5 + 2 x - 57

    if x = 2
    y = 32 +4 - 57 = negative number

    if x = 3
    y = 81*3 + 6 - 57 = positive number

    the polynomial is continuous so somewhere in there y was zero

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