Math Quiz 5

[Ether]

Originally Posted by Bryce Paputa

I'll look into an analytic solution.

It may not exist. My CAS choked on it.

[Ether]

Originally Posted by Ether

It may not exist. My CAS choked on it.

Using your R(c) method, a numerical root finder quickly converges to a precise value for c.

But you can get the same result without differentiating R(c), by simply plotting R(c) and locating the extremum.

[Bryce Paputa]

I get 3 arcsinh(2 sqrt(c)) * sqrt(4c^2+c) = 2c+8c^2. I doubt there is a nice closed form of this.

[Ether]

For completeness, here's how to solve the problem using constrained nonlinear optimization.

It's a bit easier to set up. All you need is the length and area as a function of a and b.

The area is the objective (to be maximized), and the length is a constraint on the values of a and b.

[Ether]

Extra credit:

What is wrong with this method?

[Ether]

Originally Posted by Ether

Extra credit:

What is wrong with this method?

It gives the correct answer... but what are the pros and cons compared to this method?

[Ether]

Originally Posted by Ether

It gives the correct answer... but what are the pros and cons compared to this method?

Any college students out there taking a course in numerical methods?

[Ether]

Originally Posted by Ether

Any college students out there taking a course in numerical methods?

... or multivariate calculus?