Find the Points of Inflection and Discuss the Concavity of the Function

question 16

Multiple Choice

Find the points of inflection and discuss the concavity of the function. $f ( x ) = 7 x ^ { 3 } + 8 x ^ { 2 } + 5 x - 8$

• A)inflection point at \(x = - \frac { 8 } { 21 }\) ; concave downward on \(\left( - \infty , - \frac { 8 } { 21 } \right)\) ; concave upward on \(\left( - \frac { 8 } { 21 } , \infty \right)\)
• B)inflection point at \(x = - \frac { 8 } { 21 }\) ; concave upward on \(\left( - \infty , - \frac { 8 } { 21 } \right)\) ; concave downward on \(\left( - \frac { 8 } { 21 } , \infty \right)\)
• C)inflection point at \(x = \frac { 8 } { 21 }\) ; concave downward on \(\left( - \infty , \frac { 8 } { 21 } \right)\) ; concave upward on \(\left( \frac { 8 } { 21 } , \infty \right)\)
• D)inflection point at \(x = \frac { 8 } { 21 }\) ; concave upward on \(\left( - \infty , \frac { 8 } { 21 } \right)\) ; concave downward on \(\left( \frac { 8 } { 21 } , \infty \right)\)
• E)none of the above

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Definitions:

Dollar-Value LIFO

An inventory valuation method that uses the last-in, first-out principle, adjusted for changes in the dollar value, to account for inflation.

Inventory Costs

Expenses associated with holding and managing inventory, including storage, depreciation, and insurance costs.

Year-End Costs

Expenses recognized at the end of the fiscal year, including adjustments for accruals, depreciation, and inventory valuation.

Income Manipulation

The act of altering financial statements to present a misleading view of a company's financial health or performance.