Circle and Square Min and Max

[amberzak]

A piece of string length L is to be cut into two pieces, one forms a square and the other a circle.

Where should the string be cut in order to minimise the area and where in order to maximise.

So far I have got to this point:



I know I need to do the Minimum and Maximum from here. Is that where I do the differential and set it to 0?

 

[pappus]

A piece of string length L is to be cut into two pieces, one forms a square and the other a circle.

Where should the string be cut in order to minimise the area and where in order to maximise.

So far I have got to this point:

View attachment 2007

I know I need to do the Minimum and Maximum from here. Is that where I do the differential and set it to 0?

1. Generally your way to do the question is OK.

You certainly have noticed that the graph of f is a parabola opening up. Therefore you'll get the minimum at the vertex.

2. To get the maximum you now have to check the values of f at the borders of the domain: \(\displaystyle \displaystyle{x\in \lbrack 0,L \rbrack}\)