Significance of a second partial in marginal analysis?
I'm doing a bivariate calculus problem from a textbook. I can reach all the answers, but am unsure about something -- what does an evaluated second partial derivative mean in a marginal analysis context?
Here's the question. (I won't show all the work in reaching the answers, as they are not problematic or controversial.)
Total annual profit f(x,y) is determined as
f(x,y) = 10x^3 + 20y^2 - 10xy,
when x = ad spending = 10 and
y = acres farmed = 5.
I do understand:
that f(10,5) = 10,000 = total annual profit;
that f[subscript]x = 30x^2 - 10y; and
that f[subscript]x (10,5) = 2950 = the approximate additional annual profit to be gained from increasing ad spending by one unit (i.e. from 10 to 11).
What I DON'T understand is something the author has us calculate, but which we never end up using in the analysis, and which she never comments on. Specifically, she asks for
f[subscript]xx (i.e the second partial) = 60x and
f[subscript]xx (10,5) = 600.
I can reach these answers, but I don't understand, what does 600 actually mean here?
I'd be grateful for any advice.