Posted by Marie on Monday, April 23, 2012 at 7:45pm.
finally I get to use calculus for this problem instead of completing square!
length total = 6 x
width = y
fencing = 7 y + 12 x = 480
so
y = (480-12x)/7
A = 6 x y
A = 6 (x)(480-12 x)/7
A = (6/7) (480 x - 12 x^2 )
dA/dx = (6/7)(480 - 24 x) = for max
24 x = 480
x = 20
then y = 240/7 = 34.3 approx
A = 6 x y = 6 * 20 * 240/7 = 4114.3
I have done many of these fencing problems tonight but most were in algebra where I had to find the vertex of the parabola by completing the square instead of taking the derivative and setting it to zero. Using Calculus makes it much much easier.
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