Question

Find the absolute maximum and absolute minimum of the function f(x,y)=xy−3y−9x+27 on the region on or above y=x^2 and on or below y=13.

Answer 1

Step 1: Find Critical Points
fx = y - 9 -> y = 9
fy = x-3 -> x = 3
C.P. -> (3,9)

Step 2: consider the sides
Side 1 = y = 13 with -sqrt(13)<=x<=sqrt(13)
then f(x,13) = 13x-39-9x+27 = 4x - 12
so g(x) = 4x-12, g'(x) = 4?
then I am stuck

Answer 2

try using Lagrange multipliers