Find the Equation of the Function F Whose Graph Passes $\left( 0 , \frac { 7 } { 3 } \right)$

question 56

Multiple Choice

Find the equation of the function f whose graph passes through the point $\left( 0 , \frac { 7 } { 3 } \right)$ and whose derivative is $f ^ { \prime } ( x ) = x \sqrt { 1 - x ^ { 2 } }$ .

• A) \(f ( x ) = \frac { 1 } { 3 } \left[ 8 - \left( 1 - x ^ { 2 } \right) ^ { 1 / 2 } \right]\)
• B) \(f ( x ) = \frac { 1 } { 3 } \left[ 8 - \left( 1 - x ^ { 2 } \right) ^ { 3 / 2 } \right]\)
• C) \(f ( x ) = \frac { 1 } { 3 } \left[ 10 + \left( 1 - x ^ { 2 } \right) ^ { 2 / 3 } \right]\)
• D) \(f ( x ) = \frac { 1 } { 3 } \left[ 10 + \left( 1 - x ^ { 2 } \right) ^ { 1 / 2 } \right]\)
• E) \(f ( x ) = \frac { 1 } { 3 } \left[ 10 - \left( 1 - x ^ { 2 } \right) ^ { 2 / 3 } \right]\)

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Definitions:

Point Estimate

A single value or statistic that is used to estimate the parameter of a population.

Confidence Interval

A spectrum of values obtained from sample data, expected to encompass an unknown parameter of the entire population with a certain degree of assurance.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Confidence Interval

An estimated range of values which is likely to include an unknown population parameter, calculated from a given set of sample data.