If the line
\[
2x+y=7
\]
touches the curve
\[
y=f(x)
\]
at
\[
x=\frac12,
\]
then the sum of the lengths of the normal and subnormal is
Show Hint
If the tangent at a point has slope \(m\) and the point is \((x,y)\), then
\[
\boxed{\text{Length of normal}=y\sqrt{1+m^2}}
\]
and
\[
\boxed{\text{Length of subnormal}=|my|.}
\]