A Function Is Given $G ( x ) = \frac { 3 } { x ^ { 2 } + x + 1 }$

question 40

Essay

A function is given.
(a) Find all the local maximum and minimum values of the function and the value of x at which each occurs.
(b) Find the intervals on which the function is increasing and on which the function is decreasing. State all answers correct to two decimal places.
$G ( x ) = \frac { 3 } { x ^ { 2 } + x + 1 }$

---

Definitions:

Biological Motives

Innate drives arising from biological needs that are critical for the survival and reproduction of an organism.

Social Needs

Social needs refer to the human requirement for relationships and interaction with others, including the need for belonging, love, and affection.

Human Motives

The intrinsic and extrinsic factors that drive individuals to engage in certain behaviors.

Obesity

Obesity is a medical condition characterized by an excessive amount of body fat, which poses a risk to health.