Find the Absolute Extreme Values of the Function on the Interval

question 91

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 \(\mathrm { e } ^ { - 4 } + 4\) at \(\mathrm { x } = - 4\); maximum value is \(\mathrm { e } ^ { 2 } - 2\) at \(\mathrm { x } = 2\)
• 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 \(x = 2\)
• D) Minimum value is 1 at \(x = 0\); maximum value is \(e ^ { - 4 } + 4\) at \(x = - 4\)

---

Definitions:

Configurational Information

Describes the spatial arrangement of atoms within a molecule that cannot be interconverted without breaking chemical bonds.

Cyclohexanecarbaldehyde

An organic compound consisting of a cyclohexane ring attached to a formyl group (aldehyde), C6H11CHO.

Chemotherapeutic

Relating to the treatment of disease, specifically cancer, by chemical substances or drugs.

Taxol

A complex diterpene alkaloid used as a chemotherapeutic agent, derived from the bark of the Pacific yew tree, Taxus brevifolia.