what is the average rate of change of g over the interval 0 ≤ x ≤ 9? give an exact number.
what is the average rate of change of g over the interval 0 ≤ x ≤ 9? give an exact number.
Answer
Explanation:
Step1: Find the values of (g(0)) and (g(9))
From the graph, when (x = 0), (g(0)=-7). When (x = 9), (g(9)=4).
Step2: Use the average rate of change formula
The formula for the average rate of change of a function (y = g(x)) over the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here, (a = 0), (b = 9), (g(a)=g(0)=-7), (g(b)=g(9)=4). So, (\frac{g(9)-g(0)}{9 - 0}=\frac{4-(-7)}{9}=\frac{4 + 7}{9}).
Answer:
(\frac{11}{9})