Question

Find the absolute minimum value of the function f(x,y) = 6 + 3xy -2x- 4y on the set D. D is bounded by the parabola y=x^2 and y=4

Answer 1

I found the critical point being (4/3,3/2) but when I sketch my graph, I end up with finding the minimum on the parabola but I get stuck with this f(x,x^2) = 6+3x^3 -2x-4x^2

Answer 2

Could you elaborate on the language; "on the set D"--the set D is the region bounded, the point you found is within the region, so it is the absolute minimum; regardless of the endpoints. Alternatively, you would simply plug 4/3 to x^2; no need to combine functions.

Answer 3

in cal, what we learned was to then draw the set on a graph, so l1 and l2 ( l2 being y=x^2) and then find the points within the set