Question 16537
If the cost function for producing x bars is 
{{{C(x) = 0.2X^2-3.4x+150 }}}, then to find the cost per bar, you must divide this by x.


Cost per bar= {{{(0.2X^2-3.4x+150 )/x}}}  or {{{0.2x -3.4 +150x^(-1) }}}
If you are in a calculus class (probably Calculus for Businees Majors or Concepts of Calculus!), then you take the derivative of this. 
Deriv = {{{.2 -150x^(-2) }}}


Set derivative = zero, and solve for x:
{{{.2 -150x^(-2) = 0}}}
{{{.2 - 150/(x^2) = 0 }}}
{{{.2 = 150/(x^2) }}}


Multiply both sides by the LCD {{{x^2}}}
{{{.2x^2 = 150 }}}


Divide by .2
{{{x^2 = 150/.2 = 750}}}


Square root both sides, where x>0:
x= sqrt(750)= 27.386


Unit cost= {{{(0.2X^2-3.4x+150 )/x}}}  
Unit cost (when x= 27 bars) = 7.55555. . .


R^2 at SCC