Math 3298 - Hampton - Lab 6 - Due 10/23

Lab reports should conform to the guidelines explained on the handout.  Collaboration during the lab is strongly encouraged, although the write-up of the lab report must be done individually.

Extrema of multivariable functions

Exercises

1.  Use mathematica to estimate the extreme values of f(x, y) = x^5 + y^5 + 3 x y on the constraint curve (x-3)^2 + (y-3)^2 = 9.  Some helpful commands you might want to use include Solve, ContourPlot, Plot3D, and Circle (for drawing the constraint).  It may also be helpful to try to solve this by hand as much as possible before using mathematica - be sure to include any such calculations in your lab writeup.

Here are some examples of the use of Solve and NSolve

Solve[{x + y==0,x^2-8==0},{x,y}]

NumericalSolutions=NSolve[{x + y==0,x^2-8==0},{x,y}]

{x,y}/.NumericalSolutions

The Factor command might also be useful:

Factor[x^2-9]

Here is one way to combine a contour plot with the drawing of a circle

ExamplePlot=ContourPlot[x^3+5y^2+x y + 1,{x,-1,1},{y,-1,1},DisplayFunction->Identity];
CircleRadius1=Circle[{0,0},1];
Show[ExamplePlot,Graphics[{CircleRadius1}]]