a 160-inch strip of metal 20 inches wide is to be made into a small open trough by bending up two sides on the long side , at right angles to the base. the sides will be the same height , x. if the tgrough is to have a maximum volume, how many inches should be turned up on each side? show your work
V = (20 -2x ) * x * (160) , for 0 <= x <=10
V(x) = -320*x^2+3200*x
solve dV/dx = 0
-640*x+3200= 0
3200 = 640x
x = 3200 / 640 = 5
plug in x=10 into V '' (x) = -640
V ''(5) = -640 < 0
The endpoints x= 0, x= 10 produce zero volume.
V(5) = 8000
Therefore x=5 makes a maximum volume on the interval [0,10]
is this right?
4 answers
your solution and conclusion are correct
Thank you
Someone? Be honest, you took that off of peer answer, didn't you?
they said "the longer side" so u should have used 160-2x instead of 20-2x
0 answers