$
\eqalign{
& f(x) = 2x^2 + 3x + 4 \cr
& Neem\,\,x_A = 1\,\,en\,\,x_B = 2 \cr
& A(1,9)\,\,en\,\,B(2,18) \cr
& rc_{AB} = \frac{{18 - 9}}
{{2 - 1}} = 9 \cr
& x_C = \frac{{1 + 2}}
{2} = 1\frac{1}
{2} \cr
& f\,'(x) = 4x + 3 \cr
& f\,'\left( {1\frac{1}
{2}} \right) = 9 \cr
& rc_{AB} = f\,'\left( {1\frac{1}
{2}} \right) \cr}
$ |
$
\eqalign{
& f(x) = ax^2 + bx + c \cr
& Neem\,\,x_A = p\,\,en\,\,x_B = q \cr
& A(p,ap^2 + bp + c)\,\,en\,\,B(q,aq^2 + bq + c) \cr
& rc_{AB} = \frac{{aq^2 + bq + c - ap^2 - bp - c}}
{{q - p}} \cr
& rc_{AB} = \frac{{aq^2 + bq - ap^2 - bp}}
{{q - p}} \cr
& rc_{AB} = ap + aq + b \cr
& x_C = \frac{{p + q}}
{2} \cr
& f\,'(x) = 2ax + b \cr
& f\,'\left( {\frac{{p + q}}
{2}} \right) = 2a \cdot \frac{{p + q}}
{2} + b = ap + aq + b \cr
& rc_{AB = } f\,'\left( {\frac{{p + q}}
{2}} \right) \cr}
$ |