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

question 14

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 each answer correct to two decimal places. $G ( x ) = \frac { 2 } { x ^ { 2 } + x + 1 }$

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Definitions:

Debt-to-equity Ratio

A ratio that reflects the mix of debt and equity used to finance a company's assets.

Equity Multiplier

The equity multiplier is a financial ratio that measures the proportion of a company's total assets financed by its shareholders' equity.

Price-earnings Ratio

A valuation metric for stocks, calculated by dividing the current market price of a stock by its earnings per share (EPS).

Debt-to-equity Ratio

A financial ratio indicating the relative proportion of shareholders' equity and debt used to finance a company's assets, typically used to assess leverage and financial health.