MHB [Calculus] Finished optimization problems. Would someone please check them?

[zimmertr]

Hello, I've just finished two optimization problems for my calculus class. I would really appreciate it if someone could check my work for me.

https://docs.google.com/document/d/1vcMKOg0oD0sKIrY_AzUpRrAbTsBl3nxq8vod_1dVqyE/edit?usp=sharing

 

[Ackbach]

I haven't checked every step, but the setup and overall methodology looks fine to me. Hint on Number 2: maximize $d^2$. Then you don't have to bother with square roots.

 

[Greg]

2.

$$-\dfrac{1}{2x}x+3=x^2-1\Rightarrow x=\pm\sqrt\frac72$$