Question

The table of values represents a polynomial function f(x).

Answer 1

Given:

The table of values of the function f(x).

To find:

How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4]?

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

$m=\dfrac{f(b)-f(a)}{b-a}$

The average rate of change over the interval [5, 7] is:

$m_1=\dfrac{f(7)-f(5)}{7-5}$

$m_1=\dfrac{5002-3452}{2}$

$m_1=\dfrac{1550}{2}$

$m_1=775$

The average rate of change over the interval [2,4] is:

$m_2=\dfrac{f(4)-f(2)}{4-2}$

$m_2=\dfrac{1048-230}{2}$

$m_2=\dfrac{818}{2}$

$m_2=409$

The difference between the average rate of change over the interval [5, 7] and the interval [2, 4] is:

$Difference=m_1-m_2$

$Difference=775-409$

$Difference=366$

Therefore, the average rate of change over the interval [5, 7] is 366 more than the interval [2, 4].