Convexity/ Concavity of functions

[Nikkita]

F(x1,x2)= x1¼ x2 ½

a)      Is concave

b)      Is strictly concave

c)       Convex

d)      None

(Correct Ans: b)

Are we required to do this Question by:
1st approach: using Hessian ( then ans. is coming out to be 'b' only);
2nd approach: Drawing level curves, they will depict shape of Convex function, so answer then would be 'c'..

Why are both methods contradictory to each other??

[Abhitesh]

This should be done using Hessian.
Convex level curves imply quasiconcave function. This concept is different from concave function.

[Nikkita]

Thankyou :)