Find the dimensions of the rectangle of area A sq. units that has the smallest perimeter.
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I am in Freshmen Level Calculus. We are in section 4.5 of the Salas, Hille, and Etgen book, "Calculus: One and Several Variables" 9th edition.
The name of the chapter is The Mean value theorem and its applications, But from my understanding of the examples, It does not use the MVT. The previous sections were about local extreme values, endpoint and absolute extreme values. This section is entitled "Some Max-Min Problems".
The problem is as follows:
6. Find the dimensions of the rectangle of area A sq. units that has the smallest perimeter.
Okay, I tried to work it out the same way the example did it.
I wrote two equations, Area = 2xy (Two x is the base on the x axis, the curve and the rectangle placed on a coordinate plane.) and Perimeter = 2x + 2y.
The guide to solving these type of problems in the book says the next step is to write the equation to be minimized as a function of one variable.
I keep ending up with at least two variables.
I also tried writing both x and y in the form of A and I got x = y. But that would make the rectangle a square???
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