chill bro
To find the average rates of change for the pair of functions f(x) and g(x) over the interval -5 ≤ x ≤ -2, we need to use the following formula:
Average rate of change = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the function between the given interval.
For f(x) = 2x^2, we have:
-5 ≤ x1 ≤ -2
-5 ≤ x2 ≤ -2
Let's choose two points within the interval: x1 = -5 and x2 = -2
y1 = 2(-5)^2 = 50
y2 = 2(-2)^2 = 8
Therefore, the average rate of change for f(x) over the interval is:
Average rate of change for f(x) = (y2 - y1) / (x2 - x1) = (8 - 50) / (-2 - (-5)) = -14
For g(x) = 6x^2, we have:
-5 ≤ x1 ≤ -2
-5 ≤ x2 ≤ -2
Let's choose the same two points as before: x1 = -5 and x2 = -2
y1 = 6(-5)^2 = 150
y2 = 6(-2)^2 = 24
Therefore, the average rate of change for g(x) over the interval is:
Average rate of change for g(x) = (y2 - y1) / (x2 - x1) = (24 - 150) / (-2 - (-5)) = -42
Comparing the two average rates of change, we see that the average rate of change for g(x) is greater than the average rate of change for f(x) over the interval -5 ≤ x ≤ -2. This indicates that g(x) is changing more rapidly than f(x) over this interval.