1.) Find the local maximum and minimum values and saddle
point(s) (x,y,f) of the function. If you have three-dimensional
graphing software, graph the function with a domain and viewpoint
that reveal all the important aspects of the function. (Enter your
answers as a comma-separated list. If an answer does not exist,
enter DNE.)
f (x, y) = xy − 5x − 5y − x2 − y2
2.)Find the local maximum and minimum values and saddle
point(s)(x,y,f) of the function. If...
Problem 2
Find the locations and values for the maximum and minimum of f
(x, y) = 3x^3 − 2x^2 + y^2 over the region given by x^2 + y^2 ≤
1.
and then over the region x^2 + 2y^2 ≤ 1.
Use the outline:
INSIDE
Critical points inside the region.
BOUNDARY
For each part of the boundary you should have:
• The function g(x, y) and ∇g
• The equation ∇f = λ∇g
• The set of three equations...
Find the relative maximum and minimum values.
a. f(x,y)=x^3-6xy+y^2+6x+3y-1/5
Relative minimum: ________ at ________
Relative maximum: ________ at ________
b. f(x,y)= 3x-6y-x^2-y^2
Relative minimum: ________ at ________
Relative maximum: ________ at ________