Hello,
The miminum distance in y-direction betheen the line(above) and the curve may be found like this:
we trace the parallele of the line as tangente à the curve:
-2 is the slope of the tangente if
f'(n)=-2n+5=-2
==>2n=7
==>n=7/2
The distance is -2*7/2+15 -(-(7/2)²+5*7/2)=-7+15-(-49/4+70/4)
=8-21/4=11/4=2.75