Calculate the average rate of change over the interval [−2,1] given the function f(x)=x^2−3x+2
(1 point)
Responses
To calculate the average rate of change over the interval [-2,1], we first need to find the values of the function at the endpoints of the interval.
When x = -2:
f(-2) = (-2)^2 - 3(-2) + 2
f(-2) = 4 + 6 + 2
f(-2) = 12
When x = 1:
f(1) = (1)^2 - 3(1) + 2
f(1) = 1 - 3 + 2
f(1) = 0
Now we can find the average rate of change using the formula:
Average rate of change = (f(1) - f(-2)) / (1 - (-2))
Average rate of change = (0 - 12) / (1 + 2)
Average rate of change = -12 / 3
Average rate of change = -4
Therefore, the average rate of change over the interval [-2,1] for the function f(x) = x^2 - 3x + 2 is -4.