Answer
Average rate of change (A(x)) for the function y=f(x) over interval [a, b] is given by:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
As per the statement:
x y
-1 5
1 3
4 0
To find the average rate of change for the given function from x = −1 to x = 4.
At x = -1
⇒y = 5
and
At x = 4 ,
⇒y = 0
Substitute these values we have;
[tex]A(x) = \frac{f(4)-f(-1)}{4-(-1)}=\frac{f(4)-f(-1)}{5}[/tex]
⇒[tex]A(x) = \frac{0-5}{5} = \frac{-5}{5} = -1[/tex]
Therefore, the average rate of change for the given function from x = −1 to x = 4 is, -1
