Answer:
- -4
- 503/12 ≈ 41.91667
Step-by-step explanation:
To find the average rate of change, find the change in function value, and divide that by the length of the interval.
1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4
The average rate of change of g(x) on [-1, 1] is -4.
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2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5
= (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5
= 503/12 = 41 11/12
The average rate of change of g(x) on [-2, 3] is 41 11/12.
