Respuesta :
Answer:
The average rate of change over the interval [9,10] is greater than that over the interval [5,8] by 6490.
Step-by-step explanation:
The value of f(x) = 4052 for x = 9 and f(x) = 11014 for x = 10.
Therefore, the average rate of change of f(x) with respect to x over the interval [9,10] is given by
= [tex]\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}[/tex]
= [tex]\frac{11014 - 4052}{10 - 9} = 6962[/tex]
Now, the value of f(x) = 75 for x = 5 and f(x) = 1491 for x = 8.
Therefore, the average rate of change of f(x) with respect to x over the interval [5,8] is given by
= [tex]\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}[/tex]
= [tex]\frac{1491 - 75}{8 - 5} = 472[/tex]
Therefore, the average rate of change over the interval [9,10] is greater than that over the interval [5,8] by (6962 - 472) = 6490. (Answer)
