Question

Find the average rate of change of the function f over the given interval. f(x)=x^2-6/4x-8 from x=6 to x=8

Answer 1

$f(x)=\frac{x^2-6}{4x-8} \\ \\f(8)=\frac{8^2-6}{4\times8-8}= \frac{58}{24} = \frac{29}{12} \\ \\f(6)=\frac{6^2-6}{4\times6-8}= \frac{30}{16} = \frac{15}{8} \\ \\ \frac{f(8)-f(6)}{8-6} =\frac{\frac{29}{12} - \frac{15}{8} }{2} =\frac{\frac{116}{48} - \frac{90}{48} }{2} =\frac{\frac{26}{48} }{2} =\frac{26}{96}=\frac{13}{48}$