Just want to check and see if I am setting this up right.
Let y=f(x)=x^2-6x
Find the average rate of change of y with respect to x in the interval from x=4 to x=5
(5^2-6*5)- (4^2-6*4)/ 5-4
yes, if you meant ....
((5^2-6*5)- (4^2-6*4))/( 5-4)
notice the difference between the way you typed it, and the way Google, which follows the correct order of operation, interpreted it
http://www.google.ca/#hl=en&xhr=t&q=(5%5E2-6*5)-+(4%5E2-6*4)/+5-4&cp=26&pf=p&sclient=psy&safe=off&site=&source=hp&aq=f&aqi=&aql=&oq=(5%5E2-6*5)-+(4%5E2-6*4)/+5-4+&pbx=1&bav=on.2,or.r_gc.r_pw.&fp=44e2b71c39a32254&biw=1630&bih=944
compared with
http://www.google.ca/#hl=en&xhr=t&q=((5%5E2-6*5)-+(4%5E2-6*4))/(+5-4)&cp=30&pf=p&sclient=psy&safe=off&source=hp&aq=f&aqi=&aql=&oq=((5%5E2-6*5)-+(4%5E2-6*4))/(+5-4)+&pbx=1&bav=on.2,or.r_gc.r_pw.&fp=44e2b71c39a32254&biw=1630&bih=944
which is the right way
Thanks. I am on my ipad and it is such a pain to type this stuff out. I get a little lazy.
To find the average rate of change of y with respect to x in the given interval, follow these steps:
Step 1: Calculate the value of y for x = 4:
Substitute x = 4 into the equation: y = f(x) = x^2 - 6x
y(4) = 4^2 - 6(4)
y(4) = 16 - 24
y(4) = -8
Step 2: Calculate the value of y for x = 5:
Substitute x = 5 into the equation: y = f(x) = x^2 - 6x
y(5) = 5^2 - 6(5)
y(5) = 25 - 30
y(5) = -5
Step 3: Calculate the difference in y values:
Δy = y(5) - y(4) = -5 - (-8) = 3
Step 4: Calculate the difference in x values:
Δx = 5 - 4 = 1
Step 5: Calculate the average rate of change:
Average Rate of Change = Δy/Δx = 3/1 = 3
So, the average rate of change of y with respect to x in the given interval from x = 4 to x = 5 is 3.