Question 917382
C(x)=5x^2-20x+36. find the number of automobiles that must be produced to minimize the cost.

{{{C(x)=5x^2-20x+36 }}} ...this is a parabola opening upward, completing the square to find the 
vertex 
{{{C(x)=5x^2-20x+36 }}} .........write {{{36}}} as {{{20+16}}}

{{{c(x)= 5x^2-20x+20+16}}} ...group

{{{C(x)= (5x^2-20x+20)+16}}}

{{{C(x)= 5 (x^2-4x+4)+16}}}

{{{C(x)= 5 (x-2)^2+16}}}



 Vertex({{{2}}},{{{16}}})  => {{{x= 2}}} OR {{{2000}}} automobiles


{{{drawing( 600, 600, -10, 10, -10, 50,circle(2,16,.1),locate(2,16,V(2,16)), graph( 600, 600, -10, 10, -10, 50, 5x^2-20x+36)) }}}