-- Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01)
-- find Zvu for z= f(x,y), x=uv , y= v^2 + u^2
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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.
1) Find f(x) by solving the initial value problem. f'
(x) = e x − 2x; f (0) = 2
2) A rectangular box is to have a square base and a
volume of 20f t^3 . If the material for the base costs 30¢/f t^2 ,
the material for the sides costs 10¢/ft^2 , and the material for
the top costs 20¢/f t^2 , determine the dimensions of the box that
can be constructed at minimum cost.