Use Rolle's Theorem to Show That F(x) = X³

question 530

Essay

Use Rolle's Theorem to show that f(x) = x³ + ax + b, where a > 0, cannot have more than one real root.

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Definitions:

Fair Market Value

The price that an asset would sell for on the open market between a willing buyer and seller.

Proportionate Consolidation Method

An accounting technique where an investor reports its share of an investee's assets, liabilities, income, and expenses in proportion to its ownership percentage, without consolidating the financial statements.

Consolidated Balance Sheet

A financial statement that aggregates the assets, liabilities, and equity of a parent company and its subsidiaries into one document.

Goodwill

An intangible asset that arises when a buyer acquires an existing business, representing the premium paid over the fair value of its net assets.