Math

Given the function f(x) =x^4 +6x^3 -x^2 -30x +4
Use the intermediate value theorem to decide which of the following intervals contains at least one zero.

The answers are below but i need help with the explanation please
[-5,-4]
[-4,-3]
[0,1]
[1,2]

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  1. an interval must contain at least one root if f(x) changes sign in the interval. In other words, it can't go from positive to negative without attaining the value zero somewhere in between.

    So, now you just need to check the intervals.

    f(-5) = 4
    f(-4) = -20

    So, somewhere in [-5,-4] f(x) must be zero.

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