Final answer:
The average rate of change of f(x) = -2x² + 5 is -4 from 0 to 2, -16 from 3 to 5, and 2 from -2 to 1.
Step-by-step explanation:
To find the average rate of change of a function, we can use the formula: average rate of change = (f(b) - f(a)) / (b - a), where a and b are the given values.
(a) From 0 to 2:
f(0) = -2(0)^2 + 5 = 5
f(2) = -2(2)^2 + 5 = -3
Average rate of change = (-3 - 5) / (2 - 0) = -4
(b) From 3 to 5:
f(3) = -2(3)^2 + 5 = -13
f(5) = -2(5)^2 + 5 = -45
Average rate of change = (-45 - (-13)) / (5 - 3) = -16
(c) From -2 to 1:
f(-2) = -2(-2)^2 + 5 = -3
f(1) = -2(1)^2 + 5 = 3
Average rate of change = (3 - (-3)) / (1 - (-2)) = 2