Question

For a function g(x), the difference quotient is StartFraction 6 Superscript x + h minus 3 Baseline minus 6 Superscript x + 3 Baseline Over h EndFraction. What is the average rate of change of g(x) on the interval from x = –2 to x = 1?

Answer 1

Answer:

The average rate of change in that interval is 1.99

Step-by-step explanation:

Here we have that the difference quotient for g(x) is:

$\frac{6^{x + h} - 3 - 6^x + 3}{h}$

Remember that for a general function f(x), the difference quotient is:

$\frac{f(x + h) - f(x)}{h}$

So if we look at the difference quotient for g(x), we can conclude that:

$g(x) = 6^x - 3$

Also remember that the average rate of change in an interval (a, b) is just:

$\frac{g(b) - g(a)}{b - a}$

So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:

$R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)} = \frac{6 - 6^{-2}}{3} = 1.99$

The average rate of change in that interval is 1.99