Final answer:
The average rate of change of the function f(x) = x^2 + 2x - 3 over the interval -7 < x < 3 is 0.4.
Step-by-step explanation:
The average rate of change of a function over an interval is found by taking the difference in the function values at the endpoints of the interval and dividing it by the difference in the input values. In this case, the function is f(x) = x^2 + 2x - 3 and the interval is -7 < x < 3. We can calculate the average rate of change as follows:
Average rate of change = (f(3) - f(-7))/(3 - (-7))
Plugging in the values, we get:
Average rate of change = ((3^2 + 2*3 - 3) - ((-7)^2 + 2*(-7) - 3))/(3 - (-7))
Calculating further, we get:
Average rate of change = (21 - 17)/10
Average rate of change = 4/10
Average rate of change = 0.4