Question

A furniture company wants to minimize its costs and has determined that when x

wooden chairs are built, the average cost per chair is given by
C(x)=0.01x2 -7x+1265

Answer 1

A quadratic equation like
`ax^2+bx+c` has a minimum if
`a>0` and a maximum if
`a<0` as critical points.

In both cases, the critical point has
`x` coordinate
`-(b)/(2a)`

In your case, we have
`a=0.01>0`, so the parabola has indeed a minimum, located at

`x=-(-7)/(0.01)=700`