5. Show that
A) F (x1, x2) = (2X1+3X2) ^ 2
F(x1) 2(2X1+3X2) (2)
=4(2X1+3X2)
F(X22) = 2(2x1+3x2) (2+3x2) (3)
= 6(2X1+3X2)
F (x1, x1) = (x1, x2) ^1/3 f(x12) =o
Is convex
B) F (x1, x2) = (10- X1^2- X^2 1)
-X1^2 X 2^2 +10
F(x11)=-2 F(x22) =-2 f(x12) =o
Is strictly concave
C) F (x1, x2) = (x1, x2) ^1/3
F(x11) = 1/3(x1, x1) = (x2)
F(x22) = 1/3(x1, x1) = (x1)
F (x12) =o
It is convex
D) F (x1, x2) = 2-(x1, x2) ^2
F (x 11) =4-(x1, x2) (1)
=4-(x1, x2)
F(x22) =4-(x1, x2)
F (x12) =o
Is concave