Consider the following function: f (x , y , z ) = x 2 + y...

Consider the following function:
f (x , y , z ) = x 2 + y 2 + z 2 − x y − y z + x + z

(a) This function has one critical point. Find it.
(b) Compute the Hessian of f , and use it to determine whether the critical point is a local man, local min, or neither?
(c) Is the critical point a global max, global min, or neither? Justify your answer.

Expert Solution

milcah answered 3 years ago

Given function f(x,y,z)=x^(2)+2y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2y+z=0. find the extreme value of f(x,y,z)...

Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z) and determine whether it is maximum of minimum.

Find the maximum and minimum of the function f(x, y, z) = (x^2)(y^2)z in the region...

Find the maximum and minimum of the function f(x, y, z) = (x^2)(y^2)z in the region D = {(x, y, z)|x^2 + 2y^2 + 3z^2 ≤ 1}.

Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and...

Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h are conservative?

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does...

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does not equal to 0 3. f'(0)=1 Then: a) Show that f(0)=1. (Hint: use the fact that 0+0=0) b) Show that f(x) does not equal to 0 for all x. (Hint: use y= -x with conditions (1) and (2) above.) c) Use the definition of the derivative to show that f'(x)=f(x) for all real numbers x d) let g(x) satisfy properties (1)-(3) above and let...

Consider the method of steepest descent for the function f(x, y) = x^2 − y^2 ....

Consider the method of steepest descent for the function f(x, y) = x^2 − y^2 . Note: this is a quadratic function, but the matrix Q is not positive definite. (a) Find a formula for α_k. (b) For which initial points (x0, y0) is (x1, y1) = (x0, y0)?

Consider the vector field F(x,y,z)=〈 4x^(2) , 7(x+y)^2 , −4(x+y+z)^(2) 〉. Find the divergence and curl...

Consider the vector field F(x,y,z)=〈 4x^(2) , 7(x+y)^2 , −4(x+y+z)^(2) 〉. Find the divergence and curl of F. div(F)=∇⋅F= ? curl(F)=∇×F= ?

(6) Consider the function f(x, y) = 9 − x^2 − y^2 restricted to the domain...

(6) Consider the function f(x, y) = 9 − x^2 − y^2 restricted to the domain x^2/9 + y^2 ≤ 1. This function has a single critical point at (0, 0) (a) Using an appropriate parameterization of the boundary of the domain, find the critical points of f(x, y) restricted to the boundary. (b) Using the method of Lagrange Multipliers, find the critical points of f(x, y) restricted to the boundary. (c) Assuming that the critical points you found were...

Question

Consider the following function: f (x , y , z ) = x 2 + y...

Solutions

Expert Solution

Related Solutions