Suppose $x 0$ Is an Initial Approximation of a Zero of the Function

question 105

Multiple Choice

Suppose $x 0$ is an initial approximation of a zero of the function f(x) . Using the Newton-Raphson algorithm, a second approximation, $\mathrm { x } _ { 1 }$ is obtained. Which of the following must be true?

• A) \(\mathrm { x } _ { 1 }\) is the x-coordinate of the x-intercept of the tangent line to f(x) at \(\left( { } { \mathrm { x } } _0 , \mathrm { f } \left( \mathrm { x } _ { 0 } \right) \right)\)
• B) f( \(\mathrm { x } _ { 1 }\) ) = 0
• C) \(\mathrm { x } _ { 1 }\) = \(x _0\) - \(\frac { f ^ { \prime } \left( x _ { 0 } \right) } { f \left( x _ { 0 } \right) }\)
• D) \(\mathrm { x } _ { 1 }\) is closer to the zero of f(x) than \(x _0\) .
• E) all of these

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Definitions:

Economic Profits

The financial gains that are realized when total revenues exceed total costs, including both explicit and implicit costs.

Accounting Profits

The net earnings of a company as calculated by subtracting all explicit costs from total revenues, according to standard accounting practices.

Fixed Costs

Costs that do not vary with the level of output or production, such as rent or salaries.

ATC

Average total cost is found by dividing the overall production cost by the number of units produced.