# (1) Problem 1 from SHSS 2.3 (2) For which values of a is the follo...

## Transcribed Text

(1) Problem 1 from SHSS 2.3 (2) For which values of a is the following function convex? y)=-6x2+(2a+ 4)xy-y2-4ay (3) Decide whether the following function is convex, concave, or neither: g(x,y)=x+y-e-ery. (4) Leta, b, be positive constants. Consider the Cobb-Douglas sfunctiondefinedon [(x,y, z) I x> 0,y>0,2>0} by the formula f(x,y,2)=x"ye Show that if a + b+c < 1 then f(x,y,2) is strictly concave. (5) Use Jensen's inequality to prove the following ineqality for all real numbers X1 X2: n n The right hand side is known as the root mean squared of x1 (6) Find the global minima of the following function defined on {(x,y,2) I 0,y > 0,z > 0} Justify your answer. (7) Show that f(x,y) is a convex function on R².

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