how do i know if its concave or convex?

[gibney]

i have to decide whether these functions are concave or convex and i have no idea how to do it
can someone please help me,
they are f(x,y)=(xy)^1/2
and f(x,y)=(x^1/2)(y^1/2)
thanks !!

 

[Deleted member 4993]

i have to decide whether these functions are concave or convex and i have no idea how to do it
can someone please help me,
they are f(x,y)=(xy)^1/2
and f(x,y)=(x^1/2)(y^1/2)
thanks !!

You have no idea -

How does your textbook define "concavity" for a 3-D function?

 

[gibney]

it says in my book that f is convex on I ----> f'' (x)>,_ 0 for all x in I^0
and the opposite for concave ---> <,_ 0

 

[Deleted member 4993]

it says in my book that f is convex on I ----> f'' (x)>,_ 0 for all x in I^0
and the opposite for concave ---> <,_ 0

That is in two-dimension - what about 3D?

You are doing multi-variable calculus - correct?

 

[gibney]

no its not in 3-d,,its a 2 dimensional graph and i need to just determine if its concave or convex

 

[Deleted member 4993]

no its not in 3-d,,its a 2 dimensional graph and i need to just determine if its concave or convex

You are in 3-D

your form is

z = f(x,y) = (xy)^1/2

if it were

y = f(x) - then it would be 2-D