Hi all, here are the extra credit quiz solutions. Sorry it took me a bit to crank through and make these solutions.
The optimization problem is quite a bit more computationally rigorous than many things we have done, but it is doable. Honestly, I meant to change the problem number on that one, but ended up not rendering the final changes… Sorry. But hey! Algebra practice! It builds character. Or that’s what math professors claim to tell you when they screw up 😉
You need to take special care with your interval. Since when you differentiate, you get stuff in the denominator, before you can multiply through to 0, I must ensure that I did not divide by zero. That was how I determined what the interval was. Once you get the denominator, it is at least straightforward to find the correct r. You can then plug this r back into your original constraint to find h, but time was short and so was my sheet of paper.