Use the Function Below and Its Derivative to Determine Any $f$

question 2

Multiple Choice

Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal.
$$f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 2 } , \quad f ^ { \prime } ( x ) = - 8 x ^ { 3 } + 8 x$$

• A) \(( - 1,2 ) , ( 0,0 ) , ( 1,2 )\)
• B) \(( - 1 , - 2 ) , ( 1 , - 8 )\)
• C) \(( - 1,2 ) , ( 1,2 )\)
• D) \(( 0,0 ) , ( 1,0 )\)
• E) \(( 0,0 ) , ( 1,2 )\)

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Definitions:

Sustainable Growth Rate

The maximum rate at which a company can grow its revenues and earnings without increasing financial leverage, often calculated using ROE and the dividend payout ratio.

Shareholders' Equity

Shareholders' Equity is the residual interest in the assets of a corporation after deducting its liabilities, essentially representing ownership equity.

Dividends Paid

Disbursements from a company's earnings given to its shareholders, commonly known as profit sharing.

External Financing

Funds a business obtains from outside sources, such as loans, investments, or grants, to support its operations or growth.