Show That the Curve $y = x ^ { 5 } + 2 x ^ { 3 } + 4 x$

question 186

Essay

Show that the curve $y = x ^ { 5 } + 2 x ^ { 3 } + 4 x$ has no tangent line with slope 3.

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Definitions:

Ability-to-pay Principle

A tax principle that suggests taxes should be levied according to an individual or entity's capacity to pay, reflecting their income or wealth.

Transfer Payments

Payments made by governments to individuals or other entities without the expectation of a direct return or the provision of goods or services, such as social security benefits or subsidies.

Income Distribution

The way in which a nation's total GDP is distributed amongst its population.

Quintiles

Statistical values that divide a set of data into five equal parts, often used in economic and social research to analyze distribution.