Question

The table below shows the function f.

Answer 1

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]

$=\frac{f(6)-f(2)}{6-2}$

$=\frac{f(6)-f(2)}{4}$

From the table f(6)=71

Since we want the average rate of change to be 15, we have;

$15=\frac{71-f(2)}{4}$

This implies that;

$4\times15=71-f(2)$

$60=71-f(2)$

$60-71=-f(2)$

$-11=-f(2)$

$11=f(2)$

The correct choice is A.

Answer 2

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

$R=\dfrac{g(b)-g(a)}{b-a}.$

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

$R=\dfrac{f(6)-f(2)}{6-2}\\\\\\\Rightarrow 15=\dfrac{72-f(2)}{4}\\\\\Rightarrow 15\times4=72-f(2)\\\\\Rightarrow 60=71-f(2)\\\\\Rightarrow f(2)=71-60\\\\\Rightarrow f(2)=11.$

Thus, the required value of f(2) is 11.

Option (A) is CORRECT.