(Solved): ? An open-top box is to be constructed from a 6 -in by 8 -in rectangular sheet of tin by cutting ou ...

An open-top box is to be constructed from a 6 -in by 8 -in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let $x$ denote the length of the side of each cut-out square. Assume negligible thicknéss. (a) Find a formula for the volume of the box as a function of $x$. $V(x)=$ (b) For what values of $x$ does the formula from part (a) make sense in the context of the problem? $<x<$ (c) Using technology, graph the volume function and use it to estimate the maximum volume of the box. NOTE: Round your answers to two decimal places. The maximum volume is approximately $V=$ It is attained when $x$ is approximately