Question

What is the average rate of change of the function f(x) = x^3 over the interval [-2, 3]?

a) 19
b) 21
c) 12
d) -19

Answer 1

The average rate of change of the function f(x) = x^3 over the interval [-2, 3] is 7.

Step-by-step explanation:

The average rate of change of a function is the slope of the line connecting two points on the graph of the function. To find the average rate of change of the function f(x) = x^3 over the interval [-2, 3], we 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:

Average rate of change = (f(3) - f(-2)) / (3 - (-2))

Plugging in the values, we get:

Average rate of change = (27 - (-8)) / 5 = 35/5 = 7.

Therefore, the correct answer is not listed among the options provided.