Thread: Second-order total differential

Consider the production function:
y(x1, x2) = x2/1 + x2/2

* i put the "/" signs just to show the first number above the 2nd, its not actually divided*
can someone try to explain how I go about finding the second-order total differential to find if it is concave or convex?
I'd appreciate it if you can explain as simply as possible(in words not math)

thanks a lot in advance!

Do you mean ? If so, a better notation would be y(x_1, x_2)= x_1^2+ x_2^2.

The total differential is and the "second order" total differential is 0 because there is no term "mixing" the two variables.

If the problem had been , then the total differential would have been and the second order differential would have been