Answer:
B
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 1, 6 ] and from the graph
f(b) = f(6) = 0
f(a) = f(- 1) = 0, thus
average rate of change = [tex]\frac{0-0}{6+1}[/tex] = [tex]\frac{0}{7}[/tex] = 0
The rate of change for f, in the interval -1 ≤ x ≤ 6, is 0.
Given to us,
Interval -1 ≤ x ≤ 6,
The average rate of change of any function in the closed interval [ a, b ] is given by,
[tex]\dfrac{f(b)-f(a)}{(b-a)}[/tex]
As given to us the interval here is b=6 and a=-1, thus
f(b) = f(6) = 0
f(a) = f(- 1) = 0,
The rate of change for f,
[tex]\dfrac{f(b)-f(a)}{(b-a)}\\\\\dfrac{f(0)-f(0)}{[6-(-1)]} = \dfrac{0}{7} = 0[/tex]
Hence, the rate of change for f, in the interval -1 ≤ x ≤ 6, is 0.
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