Question

What is the average rate of change of the function over the interval x = 0 to x = 6? f(x) = (2x - 1) / (3x + 5)

Answer 1

Answer:

The average rate of change of the function over the interval x = 0 to x = 6 is $\frac{34}{195}$.

Step-by-step explanation:

Geometrically speaking, the average rate of change ($r$) of the function over a given interval is determined by equation of secant line, that is:

$r = \frac{f(b)-f(a)}{b-a}$ (1)

Where:

$a$, $b$ - Lower and upper bounds.

$f(a)$, $f(b)$ - Function evaluated at lower and upper bounds.

If we know that $f(x) = \frac{2\cdot x -1 }{3\cdot x + 5}$, $a = 0$ and $b = 6$, then the average rate of change of the function over the interval is:

$f(a) = \frac{2\cdot (0)-1}{3\cdot (0) +5}$

$f(a) = -\frac{1}{5}$

$f(b) = \frac{2\cdot (6)-1}{3\cdot (6)+5}$

$f(b) = \frac{11}{13}$

$r = \frac{\frac{11}{13}-\left(-\frac{1}{5} \right) }{6-0}$

$r = \frac{34}{195}$

The average rate of change of the function over the interval x = 0 to x = 6 is $\frac{34}{195}$.