Thanks for the replies!

There's one thing I think you've done wrong however. I think you used a wrong equation for the surface. I believe it should be like this:

$\displaystyle s = 0.8 * l + 2 * 0.8 * h + 2 * h * l$

As the top of the cart is open, and the top of the carts 2 dimensions are 0.8 * the length, it should be this dimension that doesn't get timed with 2, right?

... Yes
So since $\displaystyle h * l = 25/16$ and $\displaystyle l = 25/16h$, we will get:

$\displaystyle s = 0.8 * 25/16h + 1.6 * h + 2 * 25/16$

$\displaystyle s(h) = 0.8 * 25/16h + 1.6 * h + 50/16$

Right?

... Yes
So the derivative of s'(h) will then be:

$\displaystyle s'(h) = (25/16h)^{-1} + 1.6$

... no
I think this is wrong though?