find the absolute maximum and minimum values of the following functions on the g
ID: 2848904 • Letter: F
Question
find the absolute maximum and minimum values of the following functions on the givenset R.
Optimal box Find the dimension of the largest rectangular box in the first octant of the xyz-coordinate system that has one vertices at the origin and the opposite vertex on the plane x + 2y + 3 = 6. Inconclusive tests Show that the Second Derivative text inconclusive when applied to the following functions at (0, 0). Describe the behaviour of the function at the critical point. f(x,y) = 4 + x4 + 3y4 f(x,y) = x2y - 3 f(x,y) = x4y2 f(x,y) = sin (x2y2) Absolute maxima and minima Find the absolute maximum and minimum values of the following functions on the given set R. f(x, y) = x2 + y2 - 2y +1; R = {(x, y); x2 + y2 4} f(x, y) = -x2 - y2 + 3x -y - 1; R = {(x, y): x2 + y2 6} f(x, y) = 4 + 2x2 + y2; R = {(x, y): -1 x 1, -1 y 1} f(x, y) = 6 - x2 -4y2; R = {(x, y): -2 x 2,-1 y 1} f(x,y) = x2 + y2 +4x - 2y; R = {(x, y): x2 + y2 16} f(x, y) = x2 + y2 -2x -2y; R is the closed set bounded by the triangle with vertices (0, 0),(2,0), and (0, 2). f(x,y) = x2 + 4y2 + 2x + 4y; R is the closed set bounded by the ellipse {(x, y): x = 4 cos theta, y = sin theta, for 0 theta 2pi}. f(x, y) = x2 + y2 - 2x + 2; R is the closed half disk {(x, y): x2 + y2 4 with y 0}. Absolute extreme on open and/or unbounded sets If possible, find the absolute maximum and minimum values of the followingExplanation / Answer
44).
z = sqrt(x^2 + y^2 - 2x + 2)
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