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Consider the function f(x)x^4 -32x^2 +2, -3 < or = to x < or = to 9. This function has an absolute minimum value equal to ? and an absolute maximum value equal to ?

  • calculas -

    do the first derivative, set equal to zero.

    Then at each zero, test the second derivative.

    Post back if you are lost.

  • calculas -

    As in the previous problem (quadratic), you will need to first find f'(x).
    Equate f'(x) to zero and solve for the roots. Even f'(x)=0 is a cubic equation, you can easily solve for the three roots by factorization.

    Two of the three roots fall within the given interval, so there is one maximum and one minimum, which you can check by evaluating f"(x). F"(x)>0 is a minimum and f"(x)<0 is a maximum.

    Evaluate f(x) at the two limits of the interval, as well as at the roots of f'(x)=0. These four values will give the absolute maximum and absolute minimum within the interval.

    Post your answers for checking if you wish.

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