Math

Use the IVT to show that there is a root of the equation 4x^3-6x^2+3x-2=0 between 1 and 2? (please give a full answer with steps)

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  1. The IVT states that:
    "In mathematical analysis, the intermediate value theorem states that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value." (from Wiki)
    So let
    f(x)=4x^3-6x^2+3x-2
    f(1)=-1
    f(2)=12
    and knowing that if x0 is a root, then f(x0)=0
    What can you conclude using the IVT?

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