max/min problem with areas You are given 30 meter of material which you will cut into two pieces. One piece will form an equilateral triangle, the other a rectangle whose length is three times its width. 
Where should you cut if the combined area is to minimized?  How could the combined area of these two figures be maximized? 
My work:
$A\left(x\right) = \frac{\sqrt{3}}{4}x^2 + \frac{3}{8}\left(30 - 3x \right)^2$  Fn of Area. 
Now $A^{\prime}$ is a linear function, so it can only be minimized because $A^{\prime \prime}\left(x\right) > 0$ due to the 2nd derivative test.
How can it be maximized?????

You need to use the fact that your domain is bounded.
The value of $x$, which is the length of the side of your triangle, must be at least zero, and can be at most 10 (since there are only 30 meters of material).  So the problem is to optimize your function on the interval $0 \le x \le 30$.  Find all critical points (there is just one) and evaluate the function at the critical point and the endpoints.  The maximum and minimum values will be among the resulting values.
