Find the Extreme Values of the Function and Where They $$y = \frac { \ln x } { x ^ { 2 } }$$

question 9

Multiple Choice

Find the extreme values of the function and where they occur.
- $$y = \frac { \ln x } { x ^ { 2 } }$$

• A) Maximum value is \(\frac { 1 } { 2 \mathrm { e } }\) at \(\mathrm { x } = \mathrm { e } ^ { 1 / 2 }\); minimum value is 0 at \(\mathrm { x } = 1\).
• B) Minimum value is \(\frac { 1 } { 2 \mathrm { e } }\) at \(\mathrm { x } = \mathrm { e } ^ { 1 / 2 }\); no maximum value.
• C) Maximum value is \(\frac { 1 } { 2 \mathrm { e } }\) at \(\mathrm { x } = \mathrm { e } ^ { 1 / 2 }\); no minimum value.
• D) None

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Definitions:

Affiliation Needs

A psychological concept referring to an individual's need to build relationships and feel connected to others.

Self-Actualization

The realization or fulfillment of one's talents and potentialities, regarded as a drive or need present in everyone.

Existence Needs

Basic human necessities required for survival, such as food, shelter, and safety.

Needs

Fundamental requirements or desires that drive individuals to act, ranging from basic physical needs to complex psychological motivations.