Optimization Calculus

Question

a piece of wire of length 16cm is divided into 2 parts, one forms a circle and the other forms an isosceles right triangle. How should the wire be cut so that the area is

1. maximum
2. minimum

Answer 1

This Desmos graph designates x at the circumference of the circle (opposite of video):

desmos.com/calculator/kmwdcp0b0w

Answer 2

s represents the side of the triangle

Area of triangle is (s²√3) / 4

16 - 3s represents circumference of circle.

2πr is circumference of circle

2πr = 16 - 3s

r = (16 - 3s) / 2π

Area of circle is π[(16 - 3s) / 2π]²

Add two areas, combine like terms, set first derivative to 0 and answer?