Find the extremum of f(x,y) subject to the given constraint,
and state whether it is a maximum or a minimum.
f(x,y)=(4x^2)+(3y^2)-4xy; x+y=22.Find the Lagrange function
F(x,y,lambda).Find the partial derivatives.
1. Find the local maxima of the function:
(1) f(x,y) = xy, subject to the constraint that
x+y-1=0. Result should be 1/4.
2. Find the local minima of the functions:
(1) f(x,y) = x^2+y^2, subject to the constraint that
xy-3=0. Result should be 6.
(2) f(x,y) = x^2+4xy+y^2, subject to the constraint
that x-y-6=0. Result should be -18.
Given the following utility function U(X,Y)=X0.4
Y0.6 subject to the constraint
I=XPx+YPy
find:
a the marshallian demand functions for X and Y
b the indirect utility function
c the expenditure function
d the compensated demand functions for X and Y
e from 1 and 2 establish whether x and y are inferior or normal
goods
f discuss the compensating variation, and distinguish it from
equivalent variation, for a normal and inferior good. give real
life examples
Given f(x,y) =(x3y- 2x2y)
a) find the directional derivative of f(x,y) at (1, 2) in the
direction of <-3,4>
b)find the maximum value of directional derivative at (2,4) and
the direction in which this occurs
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two
constraints x+y+z=6 and x-2*y+z=0. find the extreme value of
f(x,y,z) and determine whether it is maximum of minimum.
Given the plot of y=f(x) below, find
the plot of y=f−1(x).
A coordinate plane has a horizontal x-axis labeled from negative
7 to 7 in increments of 1 and a vertical y-axis labeled from
negative 7 to 7 in increments of 1. A curve starts at the point
left-parenthesis negative 1 comma 0 right-parenthesis, rises at an
increasing rate from left to right and passes through
left-parenthesis 1 comma 1 right-parenthesis and left-parenthesis 4
comma 6 right-parenthesis.
Select the correct...
Given the following vector force field, F, is
conservative:
F(x,y)=(2x2y4+x)i+(2x4y3+y)j,
determine the work done subject to the force while traveling along
any piecewise smooth curve from (-2,1) to (-1,0)