the area of rectangle inscribed in one arc of the graph A=2x*cos(x), 0<x<pi/2
let P be a point on the curve where rectangle touches curve
coordinates are P(x,2x*cos(x))
sides of the rectangle are
2x-> the length
y=2x*cos(x)->the height
to find max area, you need take derivative of A=2x*cos(x)
(d/dx)(2x*cos(x))=2 (cos(x) - x sin(x))
equal to zero
2 (cos(x) - x sin(x))=0
cos(x) - x* sin(x)=0....use calculator
x=0.86
then area is
A=2*0.86*cos(0.86)=1.1221924452421692
A=1.122
b.
find x for what A>=1
2x*cos(x)>=1/(2x), 0<x<pi/2
cos(x)>=1/(2x)...use calculator
0.610031<= x <=1.09801
Interval notation
[0.610031, 1.09801]
