Answer:
The average rate of change (A(x)) of f(x) over interval [a, b] is given by:
\(A(x) = \frac{f(b)-f(a)}{b-a}\) ......[1]
As per the statement:
Given the table:
x f(x)
-6 27
-3 6
-1 2
0 3
1 6
4 27
We have to find the average rate of change of f(x), represented by the table of values, over the interval [-3, 4].
At x = -3
then;
f(-3) = 6
At x = 4
then;
f(4) = 27
Substitute the given values in [1] we have;
\(A(x) = \frac{f(4)-f(-3)}{4-(-3)}\)
⇒\(A(x) = \frac{27-6}{7} = \frac{21}{7} = 3\)
Therefore, the average rate of change of f(x), represented by the table of values, over the interval [-3, 4] is, 3
