An Open Box Is to Be Constructed from a Piece $15$

question 30

Essay

An open box is to be constructed from a piece of sheet metal $15$ in by $25$ in by cutting squares of length $x$ from each corner and folding up the sides.
(a) Express the volume $V$ of the box as a function of
$x$ .
(b) What is the domain of $V$ ?
(c) Draw a graph of the function $V$ and use it to estimate the maximum volume for the box.

---

Definitions:

Lethal Weapons

Tools or instruments designed or used in a manner capable of causing death or serious bodily harm.

Depression

A common and serious medical illness that negatively affects how you feel, the way you think and how you act, offering feelings of sadness and/or a loss of interest in activities once enjoyed.

Ordinary Sadness

A normal emotional response to undesired circumstances or events, distinct from clinical depression, usually temporary and context-specific.

Specific Phobia

An intense, irrational fear of specific situations, objects, or activities, which can significantly interfere with daily functioning.