Solve the problem.
-A rectangular piece of cardboard measuring 17 inches by 45 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let $x$ represent the length of a side of each such square. For what value of $x$ will the volume be a maximum? If necessary, round to 2 decimal places.
A) $3.77$
B) $33.79$
C) $19.58$
D) $16.89$

Question

Quizplus · Accepted Answer

The volume of the box, $V$, can be expressed as a function of $x$, where $V = x(17 - 2x)(45 - 2x)$. To find the maximum volume, we differentiate this function with respect to $x$ and set the derivative equal to zero to solve for $x$. Doing so, we find that the value of $x$ that maximizes the volume is approximately $3.77$ inches.

Solve the Problem xxx Represent the Length of a Side of Each Such Square

Solve the Problem $x$ Represent the Length of a Side of Each Such Square