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

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) $f ( x ) = \frac { 1 } { 3 } \left[ 10 - \left( 1 - x ^ { 2 } \right) ^ { 2 / 3 } \right]$