Answer:
2
Explanation:
You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].
Average rate of change
The average rate of change of f(x) on the interval [a, b] is computed as ...
m = (f(b) -f(a))/(b -a)
For the given function f(x), this is ...
m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2
The average rate of change of f(x) on the interval [-7, 3] is 2.
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Additional comment
The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:
-2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.
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