Final answer:
The average rate of change of the quadratic function g(x) = -x^2 - 3x + 5 over the interval -7 to 2 is found to be 2.
Step-by-step explanation:
The average rate of change of a function on a given interval is found by subtracting the function values at the endpoints of the interval and then dividing by the difference in the endpoints' input values. So, for the function g(x) = -x^2 - 3x + 5 over the interval -7 ≤ x ≤ 2, we calculate the average rate of change as follows:
First, find the function values at the endpoints g(-7) and g(2).
- g(-7) = -(-7)^2 - 3(-7) + 5 = -49 + 21 + 5 = -23
- g(2) = -(2)^2 - 3(2) + 5 = -4 - 6 + 5 = -5
Next, subtract the function values and divide by the difference in x-values:
Average rate of change = [(g(2) - g(-7)) / (2 - (-7))]
= [-5 - (-23)] / (2 - (-7))
= 18 / 9
= 2
The average rate of change of g(x) from x = -7 to x = 2 is 2.