Answer:
A
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 ] = [ 2, 4 ], thus
f(b) = f(4) = 16 ← corresponding value of y from table
f(a) = f(2) = 4 ← corresponding value of y from table , thus
average rate of change = [tex]\frac{16-4}{4-2}[/tex] = [tex]\frac{12}{2}[/tex] = 6 → A
The average rate of change of function f(x) in the interval from x = 2 to x = 4 is 6.
The average rate of change of a function is defined as the average rate at which one quantity is changing with respect to something else changing.
[tex]A([a, b]) = \frac{f(b)-f(a)}{b-a}[/tex]
Where,
A([a, b]) is the average rate of change of function A(x) in the closed interval [a, b].
According to the given question
We have an interval [2, 4]
⇒ [a, b] = [2, 4]
Now,
f(b) = f(4) = 16 (corresponding value of f(4) from table)
and, f(a) = f(2) = 4 (corresponding value of f(2) from table)
Therefore average rate of change of f(x) in the closed interval [ 2, 4 ] is
⇒ Average rate of change of f(x) = [tex]\frac{f(4)-f(2)}{4-2}[/tex]
⇒ Average rate of change of f(x) = [tex]\frac{16-4}{2}[/tex]
⇒ Average rate of change of f(x) = [tex]\frac{12}{2}[/tex]
⇒ Average rate of change of f(x) = 6
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