Answer:
-15
Explanation:
You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].
Average rate of change
The average rate of change is defined as ...
AROC(g) = (g(b) -g(a))/(b -a)
We can evaluate this directly, or we can simplify it a bit first.
AROC = ((3b² +3) -(3a² +3))/(b -a)
= (3b² -3a²)/(b -a)
= 3(b -a)(b +a)/(b -a)
= 3(b +a)
Interval [-9, 4]
The AROC on the interval [a, b] = [-9, 4] is then ...
AROC = 3(4 +(-9)) = 3(-5)
AROC = -15
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Additional comment
In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.