The marginal cost of manufacturing a certain item is given byc′(x)=dcdx=2+0.15x. The total cost function c (x), is

[a] [Note derivative of a function is sometimes called as the marginal value, especially in economics] Given dcdx=2+0.15x Integrating we get c(x)=2x+0.15x22+D when x=0,c(x)=100⇒D=100 ∴ the required equation is c(x)=0.075x2+2x+100