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) \(1.5 \text { in. } \leq x \leq 2.5 \text { in. }\)

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Definitions:

Proactive Interference

The phenomenon where previously learned information interferes with the recall of newly learned information.

Nonsense Syllables

Sequences of letters without meaning, used in memory and learning experiments to study the mental processes involved in remembering.

Ebbinghaus

Hermann Ebbinghaus, a psychologist known for his pioneering studies on memory and the forgetting curve, illustrating how memory retention diminishes over time.

Cued Recall Task

A memory task where a participant is given prompts or cues to aid the retrieval of a specific piece of information from memory.