Explore BrainMass

Explore BrainMass

    Extreme values

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    1.)f(x,y)= 5 - 3x + 4y, D is the closed triangular region with vertices (0,0), (4,0), and (4,5)

    2.)f(x,y)= x^2 + 2xy + 3y^2, D is the closed triangular region with vertices (-1,1), (2,1), and (-1,-2)

    3.)f(x,y)= 1 + xy - x - y, D is the region bounded by the parabola y=x^2 and the line y=4

    © BrainMass Inc. brainmass.com March 4, 2021, 8:58 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/extreme-values-207537

    Solution Preview

    1. , is a closed triangular region with vertices , and . To find the maximum and the minimum of , we calculate the followings.
    , . So does not have critical points.
    , ,
    Thus the maximum value of is ; the minimum value of is .
    2. , is a closed triangular region with vertices , and . Then ...

    Solution Summary

    This provides examples of finding extreme values of a function on a set.

    $2.49

    ADVERTISEMENT