Find the average rate of change of g (x) = 2 + 3x + 10 from x = 5 to x = 7.
Simplify your answer as much as possible.
To find the average rate of change of a function over an interval, we use the formula:
Average Rate of Change = (g(7) - g(5))/(7 - 5)
First, we need to find g(7) and g(5):
g(7) = 2 + 3(7) + 10
g(7) = 2 + 21 + 10
g(7) = 33
g(5) = 2 + 3(5) + 10
g(5) = 2 + 15 + 10
g(5) = 27
Now, we can calculate the average rate of change:
Average Rate of Change = (33 - 27)/(7 - 5)
Average Rate of Change = 6/2
Average Rate of Change = 3
Therefore, the average rate of change of g(x) = 2 + 3x + 10 from x = 5 to x = 7 is 3.