Any help would be gratefully appreciated! Dunno if im making a stupid mistake and not seeing it or the answers wrong.. :L most likely the first case!
Im doing Question 2, and heres my working out:
sides of the box will be (6-x) as ive labelled. Making the total Volume of the box to be V=(6-x)(6-x)x which expanded out becomes V=x^3 - 12x^2 + 36x
differentiate that and you get dV/ds = 3X^2 - 24x + 36. Then find the stationary points, of which the maximum would be the largest volume possible point and hence the corresponding x value, which according to the question should be 1.
so you i found two stationary points, x=6 and x=2, plugging them in you see that x=2 is the maximum stationary point. pretty obvious i know when ofc if x=6, the volume would be zero.
but then this means the max volume would be if x=2 in the diagram, not x=1 like the answers suggests...? ive even plugged x=2 and x=1 into my original V (volume) equation and it shows x=2 producing a larger volume... so is there something wrong with me volume equation?
Please help TSR community... *echo community*
Volume of a Box
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