\(
\eqalign{
& f(x) = ax^2 + bx + c \cr
& I. \cr
& A:f(m) = am^2 + bm + c \cr
& B:f(n) = an^2 + bn + c \cr
& rico_{AB} = \frac{{am^2 + bm + c - \left( {an^2 + bn + c} \right)}}
{{m - n}} \cr
& rico_{AB} = \frac{{am^2 + bm + c - an^2 - bn - c}}
{{m - n}} \cr
& rico_{AB} = \frac{{a(m^2 - n^2 ) + b(m - n)}}
{{m - n}} \cr
& rico_{AB} = a\left( {m + n} \right) + b \cr
& II. \cr
& f'(x) = 2ax + b \cr
& C:f'\left( {\frac{{m + n}}
{2}} \right) = 2a \cdot \frac{{m + n}}
{2} + b \cr
& C:f'\left( {\frac{{m + n}}
{2}} \right) = a\left( {m + n} \right) + b \cr}
\)
