Let F(x) = Ax² + B, Where a and B

question 129

Essay

Let f(x) = ax² + b, where a and b are constant. Use the method of Section 3.1 to show that the slope of the tangent to the graph of f at x = x₀ is 2ax₀.

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Definitions:

Monotonic Preferences

A preference pattern where more of a good is always preferred to less, maintaining a consistent order.

Utility Function

A mathematical representation of how different combinations of goods or services lead to different levels of happiness or satisfaction for an individual.

Income

Earnings from work or investments, often measured in terms of money received over a period of time.

Utility Function

A mathematical representation of how different quantities of goods or services generate levels of happiness or satisfaction to the consumer.