Find the Particular Solution That Satisfies the Differential Equation $f ^ { \prime } ( x ) = \frac { 1 } { 2 } x - 5$

Multiple Choice

Find the particular solution that satisfies the differential equation $f ^ { \prime } ( x ) = \frac { 1 } { 2 } x - 5$ and initial condition $f ( 4 ) = - 16$ .

A) $f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 5 x$
B) $f ( x ) = \frac { 1 } { 7 } x ^ { 2 } + 5 x - 1260$
C) $f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5 x$
D) $f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5 x - 1260$
E) $f ( x ) = \frac { 1 } { 5 } x ^ { 2 } + 5 x$