9514 1404 393
Answer:
4
Step-by-step explanation:
The average rate of change of f(x) on the interval [a, b] is computed from ...
m = (f(b) -f(a))/(b -a)
On the interval [-3, 5] the average rate of change is ...
m = (f(5) -f(3))/(5 -(-3)) = ((-5^2 +6·5 +12) -(-(-3)^2 +6(-3) +12))/8
= (-25 +30 +12 +9 +18 -12)/8 = 32/8
m = 4
The average rate of change on the interval is 4.
__
Alternate solution
The first derivative of the function is ...
f'(x) = -2x +6
The average rate of change of a parabolic function on an interval is the rated of change at the midpoint of the interval. Here, the midpoint is x=(5+(-3))/2 = 1, so the average rate of change is ...
f'(1) = -2(1) +6 = 4
