calculus
posted by Daniel .
The top and bottom margins of a paster are each 6 cm and the side margins are each 4cm. If the area of printed material on the poster is fixed at 384cm^2, find the dimensinos of the poster with the smallest area.
I would like to know if my work is correct.
x = width of print
y = height of print
w = width of print
h = height of print
w = x + 8
h = y + 12
adding both sides of magins
A = wh
A = (x+8)(y + 12) xy = 384 y = 384/x
A = (x+8)(384/x + 12)
A = (x+8)([384 + 12x]/x)
A = (12x^2 + 480x + 3072)/x
domain:
x =/= 0 x > 0 cannot have negative width
(o,oo) open interval
differentiate:
A'(x) = (24x + 480)/x^2
and this is where I get stuck, x is not able to be 0 yet I keep getting 20 to make the function = 0. Is the function actually a closed interval? I am actually having a hard time figuring out if something is an open or closed interval

Your A' is wrong. I expect the quotient rule got messy. Just make it a sum of powers of x:
A = 12x + 3072/x + 480
A' = 12  3072/x^2
A' = 0 when 12 = 3072/x^2
or, x = 16
so, y = 24
The printing is 16x24 and the poster is 24x36
Respond to this Question
Similar Questions

Cal 1
The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1536 cm^2, find the dimensions of the poster with the smallest area. 
Calculus
A retangular poster is to be made out of cardboard. The margins on the top and the bottom will be 2 inches. The margins on the sides will be 1 inch. The area of the poster devoted to the printed material must be 300 square inches. … 
calulus
The top and bottom margins of a poster are 8 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area. find the … 
Calculus
The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area. 
calculus
The top and bottom margins of a rectangular poster are 6 centimeters each, and the side margins are 4 centimeters each. If the area printed on the poster is fixed at 384 cm2, a) Sketch the figure. b) Find the dimensions of the poster … 
Calculus
The top and bottom margins of a poster are 2 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area. Width = … 
Math
The top and bottom margins of a poster are 8 cm and the side margins are each 9 cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area. 
Math
The top and bottom margins of a poster are 6 cm and the side margins are each 7 cm. If the area of printed material on the poster is fixed at 384 square centimeters, find the dimensions of the poster with the smallest area. 
Math calculus
The top and bottom margins of a poster are 8 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area? 
math calculus
A poster is to contain 300 (cm square) of printed matter with margins 10cm at the top and bottom and 5cm at each side. Find the overall dimensions if the total area of the poster is minimum.