Let f be defined as follows.
y = f(x) = x^2 - 4 x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 5 to x = 5.5
For some reason I keep getting this wrong. The way I did it was: f((5.5)-f(5))/(x2-x1)= 22-5/5.5-5=34 This is wrong, could someone show me what I'm doing wrong?
for f(5.5) I got 8.25
http://www.google.ca/search?hl=en&q=5.5%5E2+-+4*5.5&btnG=Search&aq=f&aqi=&aql=&oq=
You probably had a typo in the formula, which should read:
( f(x2)-f(x1) ) / ( x2-x1 )
For the interval [5,5.5]
(f(5.5)-f(5))/(5.5-5)
=(8.25-5)/(5.5-5)
=6.5
Post again if you still have problems.
To find the average rate of change of y with respect to x in the interval from x = 5 to x = 5.5 for the given function f(x) = x^2 - 4x, you need to calculate the difference in y-values divided by the difference in x-values.
First, let's find the y-values at x = 5 and x = 5.5 using the function f(x):
For x = 5:
y = f(5) = (5)^2 - 4(5) = 25 - 20 = 5
For x = 5.5:
y = f(5.5) = (5.5)^2 - 4(5.5) = 30.25 - 22 = 8.25
Now, we can calculate the average rate of change of y with respect to x:
Average Rate of Change = (change in y) / (change in x)
Change in y = f(5.5) - f(5) = 8.25 - 5 = 3.25
Change in x = 5.5 - 5 = 0.5
Average Rate of Change = (3.25) / (0.5) = 6.5
Therefore, the average rate of change of y with respect to x in the interval from x = 5 to x = 5.5 is 6.5.