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how to use differentiation to calculate the maximum volume of a box. V 462 462 231 493 cm 3. Figure 1 The opentopped box for Example 1.
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1 volume of the box V length x width x height 30 - 2x 21 - 2x x draw a simple diagram of the piece of paper with the 4 equal squares cut out 2 V 4x2 - 102x 630 x V 4x3 -. Write this number down as length Make sure you use the same measurement for each side -- if you measure one side in inches you need to measure them all in inches. D2Vdx2-3x2 and this is negative when x is positive.
The box is formed but cutting corners.
Thus the dimensions of the desired box are 5 inches by 20 inches by 20 inches. Plugging x 3681 back into the volume formula gives a maximum volume of V 820529 in³. When the question asks to find the co-ordinates you will be expected to state both x and y values. A Show that the volume V cm 3 of the brick is given by.
