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Math Help - Application of derivative help

  1. #1
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    Application of derivative help

    How to find the absolute maximum and minimum for the function f(x)=x^3 between the limits [-2,2]?
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  2. #2
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    for a function like f(x)=x^3 there is no absolute minimum or maximum. 3rd degree polynomials have relative mins and maxs.

    Though your question is asking what's the smallest value and largest value of y=x^3, in the interval [-2,2].

    well you know the derivative of f(x)=x^3 is:

    f'(x)=3x^2

    So you know the function is always increasing, so your maximum in that interval will be where x is at its largest value.

    Since f(x) is always increasing I think you can also say the smallest value is when x is smallest. (i'm pretty sure though not 100% sure on this, it definitely makes sense though)

    does that help?
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  3. #3
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    Ya thanks that helps
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  4. #4
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    Actually, any continuous function has absolute max and min on a closed and bounded interval like [-2, 2]. They must occur where the derivative is 0, or the derivative does not exist, or at the endpoints. Since the derivative of x^3, 3x^2 always exists and is equal to 0 only at x= 0, that means you have 3 points to check.
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