Question 1112312
A quadratic function can be written in the form
{{{f(x)=ax^2+bx+c}}} ,
with constants {{{a}}} , {{{b}}} , and {{{c}}} and {{{a>0}}} ,
and has a minimum at 
{{{x=(-b)/a}}} .
In the case of {{{C(x)=4.9x^2-617.4x+19600}}} ,
{{{a=4.9}}} , {{{b=-617.4}}} and {{{c=19600}}} ;
the minimum occurs at {{{x=617.4/(2*4.9)=617.4/9.8=highlight(63)}}} ,
and at that point the value of the function is
{{{C(63)=4.9*63^2-617.4*63+19600=4.9*3969-38896.2+19600=19448.1-38896.2+19600=highlight(151.9)}}} .
 
So, the minimum of {{{C(x)}}} occurs at {{{highlight(x=63)}}} , and is {{{highlight(C(63)=151.9)}}} .
 
In reality, it does not make sense for {{{C(x)=4.9x^2-617.4x+19600}}}
to be the total cost of manufacturing {{{x}}} golf clubs.
It seems more believable that {{{C(x)=4.9x^2-617.4x+19600}}} could be the cost per club to manufacture {{{x}}} golf clubs.