Differentials: Maximums and Minimums

Question

So I'm reviewing some real-life examples of Max and Mins in differential Calculus and I'm met with an example that says that the perimeter of a square restricts the domain to (0,1). I'm not sure I understand this. Here is the page:

 

http://snag.gy/NMk9G.jpg

 

Greatly appreciate the fast answers I have been getting.

Answer 1

Adam,

 

Happy New Year.

 

You only have a 4 foot wire. If you used it all for the square, its side would be: x = 4ft/4 sides = 1 ft. and x has to be > 0 to use any wire.  So any square limits x to 0 < x ≤ 1.

 

Similarly, if it was all circle, Perimeter = 2Πx = 4, and x = 2/Π = 0.637 ft. and obviously 0 < x ≤ 0.637.

 

Since the solution might have both a square and a circle in it, or only one of them, the missing one would have x = 0.

 

Putting all this together, sets the constraint on x to 0 ≤ x ≤ 1.

Answer 2

Go back to the basic perimeter equation of 4x+2πr, which can't exceed 4, because that's all the wire you have.  If you ONLY have the square, P=4x, and if P=4, then x=1.  So with a maximum of x=1, you won't have any wire leftover for the circle.  So x must be less than 1.  Is that what you were asking?