I am currently studying for my calculus 1 final (which is on the 12th) and have reached some questions I cannot answer. For those who might have the book they are in section 8.2.8 of "Modern Engineering Mathematics 4th Edition" by Glyn James.
Question #17 States:
A wire of length L metres is bent so as to form the boundary of a sector of a circle of radius r metres and angle x radians. Show that
and prove that the area of the of the sector is greatest when the radius is L/4.
The second part of the question is not too difficult, I have managed to work through it, but I don't know how to approach the first part of the question. I have tried relating the circumference, using triangles, using the sector length formula, and other unsuccessful methods to derive that formula.
Help would be appreciated, thanks.