Find the the extreme values of \(f(x, y, z)=x-y+z\) on the unit sphere \(x^{2}+y^{2}+z^{2}=1\)
11. (5 points) Find the the extreme values of f(1, y, z) = 1 – y +z on the unit sphere 22 + y2 + x2 = 1.
Find the extreme values of subject to constraints and . f(x, y, z) y+ z = 2 We were unable to transcribe this image f(x, y, z) y+ z = 2
find extreme values E (x, y, z) = {x'+y sphere x² + y² +2²=20 ой
Find the extreme values (if any) of the function f(x,y,z) = x^2 + 2y^2 subject to the constraint x^2 + y^2 -z^2 = 1.
find the extreme values of the function f(x,y,z)=x^(2)+2y^(2 )subject to the constraint x^(2)+y^(2)-z^(2)=1
Use Lagrange's Multipliers to find the extreme values of the function f(x, y, z) = 2x + 2y + z subject to the given constraint x2 + y2 + z2 = 9.
Find the extreme values of the function subject to the given constraint. f(x y, z)=x+2y-2z x2 + y2 + 22-9 Maximum: 9 at(1, 2, -2); minimum: -9 at (-1 -2.2) Maximum: 1 atil -2 -2); minimum: -1 at (-1 2. 2) Maximum: 8 at (2.1, -2): minimum: -8 at (-2-1. 21 Maximum: 1 at (-1-2-3); minimum: -1 at(1.2.3
3. Find the local and absolute extreme values of f(x)-z + 2 cosx on [0, π] 3. Find the local and absolute extreme values of f(x)-z + 2 cosx on [0, π]
11 Find any I the extreme values (if of the given function f(x, y, 2) = x² + 2y? subject to the constraint x²+y²-2²=1 (find minimum, argue that does not exist ) maximum
Please box/circle answers Find the extreme values of the function F(x, y) = 3x2 + 5y? on the circle EXAMPLE 2 x2 + y2 = 1. SOLUTION We are asked for extreme values of f subject to the constraint 9(x, y) = x2 + y2 = 1. Using Lagrange multipliers, we solve the equations VF Ug and 9(x, y) = 1, which can be written as fx = 1gx fylgy (x,y) = 1 or as = 2x1 = 2ya x2...