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How do the average rates of change for the pair of functions compare over the given​ interval?

f(x)=2x^2
g(x)=6x^2
-5≤x≤-2
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1 Answer

4 votes

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.

User Aayush Agrawal
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