The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true
a) g(7) - g(4) = 5/6
b) bg(7 - 4)/(7 - 4) = 5/6
c) g(7) - g(4)/(7 - 4)=5/6
d) g(7)/g(4)= 5/6

Solution:

The average rate of change is defined as :

Average rate of change of function x = [g(x₂) - g(x₁)] /(x₂ - x₁)

In the problem statement given the x₂ = 7 and x₁ =4

Hence

Average rate of change of function = [g(7) - g(4)]/ (7 - 4)

Since the average rate of change is equal to 5/6 as per the problem statement we can write g(7) - g(4)/(7 - 4) = 5/6

The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true
a) g(7) - g(4) = 5/6
b) bg(7 - 4)/(7 - 4) = 5/6
c) g(7) - g(4)/(7 - 4)=5/6
d) g(7)/g(4)= 5/6

Summary:

If the average rate of change of g(x) between x = 4 and x = 7 is 5/6. The statement that must be true is g(7) - g(4)/(7 - 4) = 5/6