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VIDEO ANSWER: We will consider f of x, y, Z equal to x minus 2y plus 5z and g equal to x square plus y square plus Z square minus 30. We will write the same thing as lambda gx. We will get x equal to 1 by 2 lambda and fy equal to lambda gy from here.
SOLVED: Find the extreme values of f(x, y, z) = x^2yz + 1 on the intersection of the plane z = 6 with the sphere x^2*y^2 + z^2 = 48. The minimum of f(x, y, z) on the domain is and the maximum of f(x, y, z) on the domain is .