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?????