Finding Maximum

• Dec 3rd 2010, 10:41 AM
thainy
Finding Maximum
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)
• Dec 3rd 2010, 11:02 AM
Ackbeet
Is that

$\displaystyle \displaystyle g(s)=s\left(1-\frac{s}{k}\right),$ or

$\displaystyle \displaystyle g(x)=s\left(\frac{1-s}{k}\right)?$

Technically, you wrote the first.

What ideas have you had so far?
• Dec 3rd 2010, 11:08 AM
thainy
\displaystyle g(s)=s\left(1-\frac{s}{k}\right),

Hmmm well..... I've never taken calculus... so I don't know why our prof is even asking this question... but my first though was to take the derivative but I've never done one with two varriables before.
• Dec 3rd 2010, 11:10 AM
Ackbeet
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.
• Dec 3rd 2010, 11:27 AM
thainy
Yes I've said before.... the last time I took math was in grade 12... so... I'm not exactly sure how to do either of those things.... woud you mind giving me a hint?
• Dec 3rd 2010, 11:32 AM
Ackbeet
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?
• Dec 3rd 2010, 11:35 AM
thainy
Yes so much! thankyou!
• Dec 3rd 2010, 11:37 AM
Ackbeet
Good. Now once you have the expression looking like post # 6, how would you find the maximum?