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use the intermediate value theorem to show the polynominal function has a zero in the given interval

f(x)=x^5-x^4+3x^3-2x^2-11x+6; [1.5,1.9]

x= -2.33


after i plugged in the 1.5 and 1.9 i just want to know if my x and y are correct

  • algebra -

    i changed it too

    f(1.9)= 10.186

    f(1.5)= -2.344

  • algebra -

    so, the IVT says that if f(x) is continuous, it must take on all values between 10.186 and -2.344.

    That includes 0, so there is the proof.

    BTW, you values for f are correct.

  • algebra -

    so i am right? x and y?

    it was continuous, but they wanted it rounded to three decimal places

  • algebra -

    I wouldn't call your values x and y.

    You have two x-values: 1.5 and 1.9
    and two values for f(x) or y: -2.344 and 10.186

    and, as I said, given those two values for x, your two y values are correct to 3 places.

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