Question 435668
{{{graph(300,200,-6,6,-4,4, 4*cos(x/2))}}}


If we have a rectangle with coordinates (x,0), (-x,0), (x,4 cos(x/2)) and (-x, 4cos(-x/2)), we can say that the dimensions are 2x and 4 cos (x/2) (note that cosine is even and symmetric). Hence, our area A is equal to {{{A = (2x)(4 cos(x/2)) = 8x cos (x/2)}}}.


To find {{{dA/dx}}}, use the product rule:


{{{dA/dx = 8 cos (x/2) + 8x (-sin (x/2))(1/2) = 8 cos (x/2) - 4x sin (x/2)}}}


Then, set this to zero with x defined between {{{-pi}}} and {{{pi}}}.