Answer:
The average rate of change of the function over the interval x = 0 to x = 6 is [tex]\frac{34}{195}[/tex].
Step-by-step explanation:
Geometrically speaking, the average rate of change ([tex]r[/tex]) of the function over a given interval is determined by equation of secant line, that is:
[tex]r = \frac{f(b)-f(a)}{b-a}[/tex] (1)
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.
[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.
If we know that [tex]f(x) = \frac{2\cdot x -1 }{3\cdot x + 5}[/tex], [tex]a = 0[/tex] and [tex]b = 6[/tex], then the average rate of change of the function over the interval is:
[tex]f(a) = \frac{2\cdot (0)-1}{3\cdot (0) +5}[/tex]
[tex]f(a) = -\frac{1}{5}[/tex]
[tex]f(b) = \frac{2\cdot (6)-1}{3\cdot (6)+5}[/tex]
[tex]f(b) = \frac{11}{13}[/tex]
[tex]r = \frac{\frac{11}{13}-\left(-\frac{1}{5} \right) }{6-0}[/tex]
[tex]r = \frac{34}{195}[/tex]
The average rate of change of the function over the interval x = 0 to x = 6 is [tex]\frac{34}{195}[/tex].
