Question

A rectangle ABOD is inscribed into the region bounded by the x-axis, the y-axis and the graph y= cos2x. what is the greatest perimeter that such a rectangle can have?



Please HELP. I greatly appreciate your help.

Answer 1

let the point of contact on the cosine curve be (x,y)
So the perimeter of the rectangle
= P
= 2x + 2y
= 2x + 2cos 2x
dP/dx = 2 - 4sin 2x
= 0 for a max/min of P
4sin 2x = 2
sin 2x = 1/2
I know sin π/6 = 1/2
so 2x = π/6
x = π/12
then y = cos π/6 = √3/2

then the max of P = π/6 + 2(√3/2)
= π/6 + √3