Could some one please help me... I'm terrible at math and I need solve this for economics.
What is the maximum of the function.
its a growth formula.... and s is stock and k is a constant.
g(s) = s (1 - s/k)
I doubt that you're asked to treat k as a variable. When I see this sort of maximization problem, I think of maximizing g as a function of s (note that you have g(s), not g(s,k)). Since you have a parabola, there are two methods of solving this problem. You could do the calculus method of taking the derivative and setting it equal to zero. Or, if you feel uncomfortable with that, then just complete the square. Pick a method, and see what happens.
All right, let's complete the square, then.
The idea with completing the square is this. However, in your case, you're going to end up with something that looks like this:
$\displaystyle g(s)=-\dfrac{1}{k}(s-h)^{2}+C.$
Your goal is to find $\displaystyle h,C$ so that this holds. Make sense?