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:
[tex]\frac{6^{x + h} - 3 - 6^x + 3}{h}[/tex]
Remember that for a general function f(x), the difference quotient is:
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
So if we look at the difference quotient for g(x), we can conclude that:
[tex]g(x) = 6^x - 3[/tex]
Also remember that the average rate of change in an interval (a, b) is just:
[tex]\frac{g(b) - g(a)}{b - a}[/tex]
So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:
[tex]R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)} = \frac{6 - 6^{-2}}{3} = 1.99[/tex]
The average rate of change in that interval is 1.99
