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 ________
1. a. Find the relative maximum and minimum values of f(x, y) =
(3x^2) − (2y^2) b. Find the relative maximum and minimum values of
f(x, y) = (x^3) + (y^3) − 6xy . The expression that you may need D
= fxx(x0,
y0)fyy(x0, y0) −
(fxy(x0, y0))2
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...