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    Find all relative extrema of the following function:

    f(x) = x^3 - 6x^2 +15.

    See the attached file.

    © BrainMass Inc. brainmass.com December 24, 2021, 7:47 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/finding-relative-extrema-219124

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    Please find the solution in the attachment.

    Find all relative extrema of the following function:

    f(x) = x^3 - 6x^2 +15
    Solution:
    To find the relative extrema, we need to first differentiate the function.
    So, differentiating f(x) with respect to x, we get f'(x)=3x2-12x
    As the next step, we make f'(x) equal to zero. Then we get 3x2-12x=0. So, we get x=0 or 4
    Next, we differentiate further to get f"(x)=6x-12
    Now we have f"(0)=-12 <0. Hence the function f(x) has relative maximum at x=0
    Further, we have f"(4)=12>0. Hence the function f(x) has relative minimum at x=4.
    Hence the relative extrema of f(x) are given by f(0)=15 (relative maximum) and f(4)=-17 (relative minimum).

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:47 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/finding-relative-extrema-219124

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