Answer:
13/115.
Step-by-step explanation:
Formula for the average rate of change of a function:
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Say that b=6 and a=0.
Find the values that the function gives with these 2 values:
[tex]f(6)=\frac{2(6)-1}{3(6)+5}=\frac{11}{23} \\\\f(0)=\frac{2(0)-1}{3(0)+5}=\frac{-1}{5} \\\\[/tex]
Now we substitute these values in the formula:
[tex]A(x)=\frac{(\frac{11}{23} )-(\frac{-1}{5} )}{6-0}[/tex]
Let's solve the fraction substraction:
[tex]\frac{11}{23}- \frac{-1}{5}=\frac{11}{23}+ \frac{1}{5}=\frac{55}{115}+ \frac{23}{115}=\frac{78}{115}[/tex]
Substitute and solve the division:
[tex]A(x)=\frac{\frac{78}{115} }{6}= \frac{78}{115}*\frac{1}{6} =\frac{78}{690}=\frac{13}{115}[/tex]
