proving a function is concave

[themathman]

I am having trouble trying to prove that a function y=x^1/2, x>0 is strictly concave. I am not sure how to start this question off.

 

[Harry_the_cat]

Start by drawing a graph of the function. Does it look concave? What makes it concave?

 

[HallsofIvy]

A function is "concave" (strictly speaking "concave upward" which is the same as "convex downward") if its second derivative is positive. What is the second derivative of \(\displaystyle x^{1/2}\)?

 

[Dr.Peterson]

A function is "concave" (strictly speaking "concave upward" which is the same as "convex downward") if its second derivative is positive. What is the second derivative of \(\displaystyle x^{1/2}\)?

I think you meant, as stated here, that "concave" is the same as "concave downward". It always feels backward to me, even though I know the reason ...