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    Convexity and extreme values

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    Check that the function:
    f(x1, x2, x3) = (x1)^2 + (x2)^2 + (x3)^2 - x1 - x2 - x3
    is convex. Find the extreme values of f under the conditions:
    (x1)^2 + (x2)^2 = 4, -1 <= x3 <= 1. (x3 goes from -1 to 1)

    © BrainMass Inc. brainmass.com October 9, 2019, 10:04 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/convexity-extreme-values-207308

    Solution Preview

    see attached

    f(x1, x2, x3) = (x1)^2 + (x2)^2 + (x3)^2 - x1 - x2 - x3
    is convex. Find the extreme values of f under the conditions: ...

    Solution Summary

    This provides an example of checking that a function is convex and finding extreme values.

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