calculate the average rate of change over the interval [-2,1] given the function f(x)=x^2+2x-2
a.-4
b.1
c.3
d.-1
Let's first find the average rate of change formula:
Average rate of change of a function f(x) over an interval [a, b] is given by:
(f(b) - f(a))/(b - a)
In this case, f(x) = x^2 + 2x - 2, a = -2, and b = 1.
f(-2) = (-2)^2 + 2(-2) - 2 = 4 - 4 - 2 = -2
f(1) = 1^2 + 2(1) - 2 = 1 + 2 - 2 = 1
Now, plug these values into the formula:
Average rate of change = (f(1) - f(-2))/(1 - (-2))
Average rate of change = (1 - (-2))/(1 + 2)
Average rate of change = (1 + 2)/3
Average rate of change = 3/3
Average rate of change = 1
Therefore, the average rate of change of the function f(x) = x^2 + 2x - 2 over the interval [-2,1] is 1.
The correct answer is:
b. 1