(Solved): A box with a square base and open top must have a volume of 219,488cm^(3). We wish to find the dimen ...
A box with a square base and open top must have a volume of
219,488cm^(3). We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only
x, the length of one side of the square base. [Hint: uco the volume formula to express the height of the box in terms of
x.]
A(x)=Next, find the derivative,
A^(')(x).
A^(')(x)=Part 2 of 2 At this point we know that
A^(')(x)=2x-4(219488)/(x^(2)). Now, find the value of
rthat makes the derivative zero.
A^(')(x)=0when
x=We next have to make sure that this value of
xgives a minimum value for the surface area. Let's use the second derivative test. Find
A^('')(x).
A^('')(x)=Evaluate
A^('')(x)at the
x-value you gave above. NOTE: Your last answer above should be positive; this means that the graph of
A(x)is concave up around that value, so the zero of
A^(')(x)indicates a local minimum for
A(x). Question Help: Written Example Let
log(A)=-1,log(B)=2, and
log(C)=8. Evaluate the following logarithms using logarithmic properties.
log((A^(5))/(\sqrt(B)))=
◻
log((B)/(C^(4)))=
◻
log((A)/(B^(2)C))=
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