Answer:
Option B is correct
-2.3
Step-by-step explanation:
Average rate of change(A(x)) for the function f(x) over the interval [a, b] is given by:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex] ....[1]
We have to find the average rate of change from x = 1 to x = 4.
From the graph as shown below
For x = 1
f(1) = 3
and
For x = 4
f(4) = -3.9
Using [1] we have;
[tex]A(x) = \frac{f(4)-f(1)}{4-1}[/tex]
Substitute the given values we have;
[tex]A(x) = \frac{-3.9-3}{3}[/tex]
⇒[tex]A(x) = \frac{-6.9}{3}[/tex]
Simplify:
[tex]A(x) = -2.3[/tex]
Therefore, -2.3 value is closest to the average rate of change from x = 1 to x = 4
