Asked by Joan
AN OPEN BOX IS TO BE MADE FROM A CARDBOARD 20 INCHES BY 14 INCHES, BY CUTTING A SQUARE FROM EACH CORNER AND FOLDING UP THE SIDES. FIND THE DIMENSIONS OF THE BOX THAT WILL MAXIMIZE THE VOLUME OF THE BOX
Answers
Answered by
oobleck
OK! STOP SHOUTING
If an x-inch square is cut from each corner, the volume is
v = (20-2x)(14-2x)*x = 4(x^3 - 17x^2 + 70x
dv/dx = 4(3x^2 - 34x + 70)
So max volume is when x = (17-√79)/3
now you can finish it off
If an x-inch square is cut from each corner, the volume is
v = (20-2x)(14-2x)*x = 4(x^3 - 17x^2 + 70x
dv/dx = 4(3x^2 - 34x + 70)
So max volume is when x = (17-√79)/3
now you can finish it off
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