Question

2. Perform 2 iterations of Newton’s method on f(x,y)=x^4+4x^2*y+4y^2+2x+2y starting at(1,1).

Answer #1

Perform two iterations of the gradient search method on f(x,y)=
x2+4xy+2y2+2x+2y. Use (0,0) as a starting
point. You must do this by hand. Please find the optimal λ* by
taking the derivative and setting it equal to 0.

Complete four iterations of Newton’s Method for the function
f(x)=x^3+2x+1 using initial guess x1= -.5

Solve using elimination method:
x-2y+3z =4
2x-y+z = -1
4x + y + z = 5
What is z in the solution?

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

Find the maximum and minimum values of f(x,y,z)=2x-2y-z on the
closed and bounded set 4x^2+2y^2+z^2 ≤ 1

Construct a convergent Jacobi iteration to the
system
x+5y+2z=2
(45+13)x-2y+10z=3
-4x+3y-(45+8)z=4,
Perform two iterations.

f(x,y) = x^2+y^2+4x-4y
Find the extreme values of f on the circle x^2+y^2 = 9 by using
Lagarange Multiplier method and find where does f have maxima and
minima on the dis x^2+y^2 <=9

Calculate ZZ D f(x, y) dA as an iterated integral, where f(x, y)
= −4x 2y 3 + 4y and D is the region bounded by y = −x − 3 and y = 3
− x 2 . SHOW ALL YOUR WORK!

find the directional derivative of f(x,y) = x^2y^3 +2x^4y at the
point (3,-1) in the direction theta= 5pi/6
the gradient of f is f(x,y)=
the gradient of f (3,-1)=
the directional derivative is:

consider the 2 variable function f(x,y) = 4 - x^2 - y^2 - 2x -
2y + xy
a.) find the x,y location of all critical points of f(x,y)
b.) classify each of the critical points found in part a.)

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