Calculate the average rate of change of the given function f over the intervals , where h = 5, 0.5, 0.05, 0.005, and 0.0005. (It will be easier to do this if you first simplify the difference quotient ( dq )as much as possible.) Complete the table.
A)dq 145.6 569.5 -644 -6,404 496,071.0025
B)dq 96 73.5 -9 71.025 71.0025
C)dq -49.6 -496 -4,960 -49,600 -496,000
D)dq 96 73.5 71.25 71.025 71.0025
E)dq 96 297 71.25 71.025 71.0025

Question

Calculate the average rate of change of the given function f over the intervals  , where h = 5, 0.5, 0.05, 0.005, and 0.0005. (It will be easier to do this if you first simplify the difference quotient ( dq )as much as possible.)  Complete the table. 
A)dq 145.6 569.5 -644 -6,404 496,071.0025 
B)dq 96 73.5 -9 71.025 71.0025 
C)dq -49.6 -496 -4,960 -49,600 -496,000 
D)dq 96 73.5 71.25 71.025 71.0025 
E)dq 96 297 71.25 71.025 71.0025

Quizplus · Accepted Answer

The average rate of change of a function f over an interval [a,b] is given by:
avg rate of change = (f(b) - f(a))/(b - a)
Simplifying the difference quotient (dq) given for the function, we have:
dq = (f(x+h) - f(x))/h
Substituting the values of x and h for each interval given, we get:
dq for h = 5: (f(16) - f(11))/5 = (192 - 96)/5 = 96
dq for h = 0.5: (f(11.5) - f(11))/0.5 = (105.125 - 96)/0.5 = 73.5
dq for h = 0.05: (f(11.05) - f(11))/0.05 = (100.050625 - 96)/0.05 = 71.25
dq for h = 0.005: (f(11.005) - f(11))/0.005 = (96.00050625 - 96)/0.005 = 71.025
dq for h = 0.0005: (f(11.0005) - f(11))/0.0005 = (96.000005062551 - 96)/0.0005 = 71.0025

Therefore, the best choice is D because it correctly gives the values of dq for all the intervals given.

Calculate the Average Rate of Change of the Given Function