Let f (x) = x2+6x+11 .

What is the average rate of change from x = 5 to x = 8?

19.

To find this you first have to find the f (x) values for x = 5 and x = 8

x = 5

f (x) = 5^2 + 6 (5) + 11

f (x) = 25 + 30 + 11

f (x) = 66

x = 8

f (x) = 8^2 + 6 (8) + 11

f (x) = 64 + 48 + 11

f (x) = 123

Then you subtract the two from each other to see how much it has changed in those 3 numbers.

123 - 66 = 57.

Then you take that answer and divide it by the change in x (which is 3)

57/3 = 19