L = 13 - 2x
w = 11 - 2x
V = (13-2x)(11-2x)x
V = (143 - 48 x + 4 x^2)x
V = 4 x^3 -48 x^2+143 x
find where dV/dx = 0
0 = 12 x^2 - 96 x + 143
x = [ 96 +/- sqrt(9216-6864)]/24
x = [96 +/- 48.5 ]/24
x = 1.98 in
or
x = 6.02 (too big, no width left)
so about 2 inches high
A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with
side length x from each corner and folding up the sides.
a. Find a formula for the volume of the box in terms of x
b. Find the value for x that will maximize the volume of the box. Round to 2 decimal places if needed.
1 answer
4 answers