Answer
$$C\left( x \right) = 2{x^2} - 5x + 8$$
Work Step by Step
$$\eqalign{
& C'\left( x \right) = 4x - 5;{\text{ fixed cost is }}\$ {\text{8}} \cr
& {\text{The marginal function cost is the derivative of the function cost }}C'\left( x \right) \cr
& {\text{then}}{\text{, the function cost }}C\left( x \right){\text{ is }} \cr
& C\left( x \right) = \int {C'\left( x \right)} dx \cr
& {\text{replacing }}4x - 5{\text{ for }}C'\left( x \right) \cr
& C\left( x \right) = \int {\left( {4x - 5} \right)} dx \cr
& {\text{integrating}} \cr
& C\left( x \right) = 2{x^2} - 5x + K{\text{ }}\left( {\bf{1}} \right) \cr
& \cr
& {\text{Find }}K,{\text{we know that the fixed cost is }}\$ {\text{8 then }}C\left( 0 \right) = 8 \cr
& 8 = 2{\left( 0 \right)^2} - 5\left( 0 \right) + K \cr
& 8 = K \cr
& {\text{then substituting }}K = 8{\text{ into the equation }}\left( {\bf{1}} \right){\text{ we obtain}} \cr
& C\left( x \right) = 2{x^2} - 5x + 8 \cr} $$
