Showing a Function is Convex

[buckley]

My homework question is to show that the following function is strictly convex. I'm not asking someone to work it out for me, but how do I show it... if I take all second derivatives, this gives me a function for each. Help!

\(\displaystyle f(x_1,x_2,x_3)=e^{x_1^2+x_2^2+x_3^2}\)

 

[Deleted member 4993]

My homework question is to show that the following function is strictly convex. I'm not asking someone to work it out for me, but how do I show it... if I take all second derivatives, this gives me a function for each. Help!

\(\displaystyle f(x_1,x_2,x_3)=e^{x_1^2+x_2^2+x_3^2}\)

Can you show:

\(\displaystyle f(x) \ = \ e^{x^2}\)

is strictly convex?

 

[buckley]

Is this just showing that the second derivative is nonpositive for all x?

Is it satisfactory to just say that the function that we find when we take the second derivative is nonpositive for all x?