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

question 57

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.
$G ( x ) = \frac { 2 } { x ^ { 2 } + x + 1 }$

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Definitions:

Oct-1-ene

A linear alkene with the double bond starting from the first carbon atom.

Resonance Structures

Different ways of drawing the same molecule that depict the possible locations of pi electrons or nonbonded electrons within the molecule.

Regiochemistry

This term relates to the orientation of the addition or substitution of a chemical bond in a molecule, determining the structure of the resulting product.

Cycloaddition

A chemical reaction in which two or more unsaturated molecules (or parts of the same molecule) combine to form a cyclic compound.