# 0-15 - CHAP 0 Mathematical Preliminaries 17 15 A function...

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CHAP 0 Mathematical Preliminaries 17 15. A function f ( x , y , z ) of x, y, and z is defined as     1 ( , , ) [ ] { } 10 2 x f x y z x y z y x y z z     KR where 1 2 3 1 [ ] 2 4 5 and { } 2 3 5 6 1       (a) Multiply the matrices and express f as a polynomial in x, y, and z. (b) Write down the three equations necessary to find the extreme value of the function in the form 3 3 3 1 31 [ ] { } x y z  Ab . (c) Solve the equations in (b) to determine x, y, and z corresponding to the extreme value of f . (d) Compute the extreme value of f. (e) Is this a maxima or minima? (f) Compute the determinant of [ K ]. Solution: (a) 222 1 2 3 2 3 5 2 10 2 f x y z xy xz yz x y z ; (b) 1 2 3 1 2 4 5 2 3 5 6 1 x y z                                               ; (c) 3

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0-15 - CHAP 0 Mathematical Preliminaries 17 15 A function...

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