Answer:
A. 11
Step-by-step explanation:
The average rate of change of the given function over the interval [2,6] is simply the slope of the secant line connecting the point (2,f(2)) and (6,f(6)).
This implies that, the average rate of change over [2,6]
[tex]=\frac{f(6)-f(2)}{6-2}[/tex]
[tex]=\frac{f(6)-f(2)}{4}[/tex]
From the table f(6)=71
Since we want the average rate of change to be 15, we have;
[tex]15=\frac{71-f(2)}{4}[/tex]
This implies that;
[tex]4\times15=71-f(2)[/tex]
[tex]60=71-f(2)[/tex]
[tex]60-71=-f(2)[/tex]
[tex]-11=-f(2)[/tex]
[tex]11=f(2)[/tex]
The correct choice is A.
Answer: The correct option is (A) 11.
Step-by-step explanation: Given the following table that shows the function f :
x 2 3 4 5 6
f(x) ? 15 23 39 71
We are to determine the value of f(2) that will lead to an average rate of change of 15 over the interval [2, 6].
We know that
the rate of change of a function g(x) over an interval [a, b] is given by
[tex]R=\dfrac{g(b)-g(a)}{b-a}.[/tex]
From the table, we note that
f(6) = 71 and f(2) = ?
So, the rate of change of the function f(x) over the interval [2, 6] is given by
[tex]R=\dfrac{f(6)-f(2)}{6-2}\\\\\\\Rightarrow 15=\dfrac{72-f(2)}{4}\\\\\Rightarrow 15\times4=72-f(2)\\\\\Rightarrow 60=71-f(2)\\\\\Rightarrow f(2)=71-60\\\\\Rightarrow f(2)=11.[/tex]
Thus, the required value of f(2) is 11.
Option (A) is CORRECT.
