Find the Absolute Extreme Values of the Function on the Interval

question 74

Multiple Choice

Find the absolute extreme values of the function on the interval.
- $$f ( x ) = e ^ { x } - x , - 4 \leq x \leq 2$$

• A) Minimum value is 1 at \(x = 0\); maximum value is \(\mathrm { e } ^ { - 4 } + 4\) at \(x = - 4\)
• B) Minimum value is 1 at \(x = 0\); no maximum value
• C) Minimum value is 1 at \(x = 0\); maximum value is \(\mathrm { e } ^ { 2 } - 2\) at \(\mathrm { x } = 2\)
• D) Minimum value is \(\mathrm { e } ^ { - 4 } + 4\) at \(\mathrm { x } = - 4\); maximum value is \(\mathrm { e } ^ { 2 } - 2\) at \(\mathrm { x } = 2\)

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Definitions:

Theoretical Minimum

The lowest possible amount of energy that a quantum mechanical physical system may have.

Product-Oriented Layout

An arrangement of resources in a production facility where equipment and staff are positioned according to the sequence of operations.

Line Balancing

The process of assigning work to different stations in a production line to ensure each has an approximately equal amount of work and minimize idle time.

Daily Capacity

The total amount of production output or services that an organization can achieve within a single day.