1. ## Related rates

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Any pointers? I can't see how to relate $h$ to $\ell$.

2. Notice that it is asking you to "minimize" therefore this is an optimization problem, not related rates.

3. Oops!

Yes, indeed. But c should eventually be a single variable function, so I need to find a way to eliminate one of the variables.

4. Any tips on this? I'm kinda stuck.

5. I too find this problem hard but I can assist you with what I know:

Notice that they ask you to minimize, thus you have to find c'(h), then set c'(h)=0 and when you have found that h, use c''(h) to see which solutions are minimum or maximum.
I don't think you have to relate h to l since l was given as a constant, and they also tell you that your answer for h will be in terms of l.

Again, I'm not completly sure but I hope I helped.

6. Oh. I was under the impression that $\ell$ was variable?

Also, don't we need to somehow use that information about the density, rho?

I do know about finding critical points of a function, but I'm certain that I first must eliminate one of the variables, since this is a single-variable calculus subject, and there are no partials here.