Answer:
Explanation:
You want to compare the average rates of change on the interval [-6, -3] of the functions f(x) = 4x² and g(x) = 8x².
Average rate of change
The average rate of change of p(x) on the interval [a, b] is given by ...
ARC = (p(b) -p(a))/(b -a)
F(x)
The average rate of change is ...
ARC = (f(-3) -f(-6))/(-3 -(-6))
ARC = (36 -144)/3 = -108/3 = -36
The average rate of change of f(x) on [-6, -3] is -36.
G(x)
The average rate of change is ...
ARC = (72 -288)/3 = -216/3 = -72
The average rate of change of g(x) on [-6, -3] is -72.
Comparison
The ratio of the rates of change is ...
ARC(g(x))/ARC(f(x)) = -72/-36 = 2
The average rate of change of g(x) is 2 times that of f(x).
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Additional comment
We hope you noticed that g(x) is f(x) scaled vertically by a factor of 2. That scale factor is the ratio of the rates of change of the two functions.