For the Function $f ( x ) = 2 x ^ { 2 } - x$

question 118

Essay

For the function $f ( x ) = 2 x ^ { 2 } - x$
determine the average rate of change between the values $x = - 1$
and $x = 0$

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Definitions:

Natural Monopoly

A market condition where due to high fixed or start-up costs, efficient service is provided by a single firm instead of multiple competing firms, often seen in utilities sectors.

Fair-Return Price

For natural monopolies subject to rate (price) regulation, the price that would allow the regulated monopoly to earn a normal profit; a price equal to average total cost.

Allocatively Efficient

A state of resource allocation in which it is impossible to make any one individual better off without making someone else worse off.

Socially Optimal Price

The price of a good or service that reflects the external costs and benefits to society, aiming to achieve the most efficient allocation of resources.