Given the Interval $( a , b )$ On The $x$ -Axis with the Point

question 174

Multiple Choice

Given the interval $( a , b )$ on the $x$ -axis with the point $c$ inside, find the greatest value for $\delta > 0$ such that for all $x$ ,
$0 < | x - c | < \delta \Rightarrow a < x < b \text {. }$
- $$a = \frac { 3 } { 9 } , b = \frac { 8 } { 9 } , c = \frac { 4 } { 9 }$$

• A) \(\delta = 1\)
• B) \(\delta = \frac { 1 } { 9 }\)
• C) \(\delta = 0\)
• D) \(\delta = \frac { 4 } { 9 }\)

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Definitions:

Diminishing Returns

A rule that asserts when one input in the production process is augmented without changes to the others, there will ultimately be a decline in output after reaching a specific level.

Average Fixed Cost

The cost per unit that remains constant regardless of the level of production or output.

Output

The total amount of goods or services produced by a company or economy.

Total Cost

The total expense incurred in the production of goods or services, including both fixed and variable costs.