Final answer:
To find the average rate of change of a function over an interval, calculate the difference in the function values at the endpoints and divide by the difference in the x-values.
Step-by-step explanation:
To find the average rate of change of a function over an interval, you need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values. In this case, the function is f(x) = 2x³ - 4x² + 5x - 2 and the interval is [2, 4].
First, find the function values at the endpoints of the interval:
f(2) = 2(2)³ - 4(2)² + 5(2) - 2
f(2) = 2(8) - 4(4) + 10 - 2
f(2) = 16 - 16 + 10 - 2
f(2) = 8
f(4) = 2(4)³ - 4(4)² + 5(4) - 2
f(4) = 2(64) - 4(16) + 20 - 2
f(4) = 128 - 64 + 20 - 2
f(4) = 82
Then, calculate the difference in function values:
82 - 8 = 74
Finally, divide the difference in function values by the difference in x-values:
(f(4) - f(2)) / (4 - 2) = 74 / 2 = 37
Therefore, the average rate of change of the function over the interval [2, 4] is 37.