Math
posted by Chole on .
The area of a rectangular photograph is 59 square inches.It is to be mounted on a rectangular card with a boarder of 1 inch at each side and 2 inches at the top and bottom.Express the total area of the photograph and the boarder,A, as a function of the width of the photograph,x.what width produces the maximum area

let p = area of photo = 59
let x be the width. So, the height is 59/x
m = (x+2)(59/x + 4)
m = 59 + 118/x + 4x + 8
to find max mounted area, set m' = 0
m' = 118/x² + 4 = (4x²  118)/x^2
So, m' = 0 when 4x²118 = 0
x²  29.5 = 0
x = 5.43"