Final answer:
To calculate the average rate of change of a function, find the difference in function values divided by the difference in input values for each interval given. The average rate of change from -4 to -3 is -50, from -2 to 4 is 10, and from 4 to 5 is 145.
Step-by-step explanation:
To find the average rate of change of a function, we need to calculate the difference in the function values divided by the difference in the input values. Let's calculate it for each interval:
(a) From -4 to -3:
Change in function values: f(-3) - f(-4) = (-27 - 23) = -50.
Change in input values: -3 - (-4) = 1.
Average rate of change: -50 / 1 = -50.
(b) From -2 to 4:
Change in function values: f(4) - f(-2) = (61 - 1) = 60.
Change in input values: 4 - (-2) = 6.
Average rate of change: 60 / 6 = 10.
(c) From 4 to 5:
Change in function values: f(5) - f(4) = (146 - 1) = 145.
Change in input values: 5 - 4 = 1.
Average rate of change: 145 / 1 = 145.
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