Question

Find an absolute max for the function f(x,y)=xy defined on the region D={(x,y)/ x^2/16+y^2<=1}.

Do this problem two ways:

first by finding the critical point(s) and parametrizing boundary

and then, by using Lagrange multipliers.

State what you learned about the Lagrange method from having these two sets of solutions.

Answer #1

Consider the function f(x, y) = xy and the domain D = {(x, y) |
x^2 + y^2 ≤ 8}
Find all critical points & Use Lagrange multipliers to find
the absolute extrema of f on the boundary of D,which is the circle
x^2 +y^2 =8.

I have a question that relates to 14.7 from the Stewart Calculus
book regarding absolute max and min of a triangular region.
Boundaries of triangle: y=x, x=0, y=4, and the function is: f(x,y)
= x^2-xy+y^2+1
I got as far as finding the critical point of (0,0) solving for
fx=0 and fy = 0, but I am struggling to find the critical points
along the boundary and solve the rest of the problem. Any help
would be appreciated :)

The function f(x,y)=4x-4y has an absolute maximum value and
absolute minimum value subject to the constraint x^2-xy+y^2=9. Use
Lagrange multipliers to find these values.

Find the absolute extrema (absolute max/min) of ?(?, ?) = ?? − ?
− 2? + 8 on the triangular region ? with vertices (0,0), (4,0), ???
(0,4). Draw the region and call the boundary on the x-axis ?1 (?,
?), the boundary on the y-axis ?2 (?, ?), and the boundary on the
diagonal of the triangle ?3 (?, ?). Note: Re-write each boundary as
a function of one-variable.

Find the absolute maximum and minimum values of the function f
(x, y) = x^2 xy+on the region R bounded by the graphs of y = x^2
and y = x+ 2

f(x,y)=xy ; 4x^2+y^2=8
Use Lagrange multipliers to find the extreme values of the
function subject to the given constraint.

Find the absolute min and max values of the function
f(x, y) =x + y− x^2y on the closed triangular region with
vertices (0,0), (3,0), and (0,3).

Find the absolute maximum, and minimum values of the function:
f(x, y) = x + y − xy Defined over the closed rectangular region D
with vertices (0,0), (4,0), (4,2), and (0,2)

Use Lagrange multipliers to find the maximum value of the
function f(x,y) = xy given the constraint x+y=10

. Find the absolute max and min of the following function f(x,
y) = x^2 + 2xy − y^2 − 4x, 0 ≤ x ≤ 2, 0 ≤ y ≤ 2.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago