Final answer:
To determine the average rate of change of the function f(x) = x² + 14x from x = –11 to x = 8, use the difference quotient by finding f(x + h) and f(x), then dividing the difference by the change in x (h). The average rate of change is calculated as 11 units.
Step-by-step explanation:
To determine the average rate of change of the function f(x) = x² + 14x from x = –11 to x = 8, you can use the difference quotient formula which is given by f(x + h) – f(x) divided by h, where h is the change in the value of x. In Moira's case, h would be the difference between the two x-values: 8 - (-11) = 19. You would plug in x and x + h into the original function to find the values of f(x) and f(x + h) respectively.
To find f(x + h), first replace x with x + h in the equation and simplify:
f(x + h) = (x + h)^2 + 14(x + h)
Then, Moira can calculate the difference quotient to find the average rate of change:
f(8) = 8² + 14*8 = 64 + 112 = 17
Thus, the average rate of change of the function from x = –11 to x = 8 is 11 units.