An Open-Top Box Is to Be Made by Cutting Small $V ( x ) = 144 x - 48 x ^ { 2 } + 4 x ^ { 3 }$

question 154

Multiple Choice

An open-top box is to be made by cutting small identical squares from each corner of a 12 -by-12-in. sheet of tin and bending up the sides. If each corner square is x inches on a side, the volume of the box (in in. ³) is given by $V ( x ) = 144 x - 48 x ^ { 2 } + 4 x ^ { 3 }$ . By sketching the graph of V(x) , estimate what values of x result in a box with a volume greater than 64 in³ .

• A) \(1.0 \text { in. } \leq x \leq 3.0 \text { in }\)
• B) \(0.1 \text { in. } \leq x \leq 5.0 \text { in }\)
• C) \(0.54 \text { in. } \leq x \leq 4 \text { in. }\)
• D) \(1.5 \text { in. } \leq x \leq 2.5 \text { in. }\)

---

Definitions:

Development

The process of growth and change that a person undergoes, which can be physical, cognitive, or emotional.

Freud

Sigmund Freud, an Austrian neurologist and the founder of psychoanalysis, known for his theories on the unconscious mind and the development of psychosexual stages.

Latent Content

The unconscious meaning of a dream.

Manifest Content

The outward content of a dream.