[Global Optimization on Domains] [P] Find the absolute maximum and minimum values of the function on the described domain. When checking for extrema on any boundaries, you may choose whether you want to use a parametrization or Lagrange Multipliers; some problems might be easiest when using a combination. (a)f(x,y)=x^2 −y^2 −2xy−2x, on the triangular region whose vertices are(1,0),(0,1), and(−1,0). (b)g(x,y)=x+xy−2y^2, on the domainy≥0,y≤ x ,x≤1. (c)h(x,y)=e^xy, on the disk(x/2 )^2 +y^2 ≤1. t† If you use your answers to part (a) and part (b) to justify why this is a maximum, you don't have to do the second rivative test. (d)f(x,y)=xy, on the part of the curve2x^3 +y^3 =16which is in the first quadrant (including endpoints). (e)g(x,y)=x^2 +3y, on the line segment from(−2,2)to(2,−2). (f)h(x,y,z)=x+2y+3z, on the unit sphere.
