Question

What is the average rate of change of f(x) from x₁=5 to x₂=10 ? Please write your answer as an integer or simplified fraction. f(x)=6x 3

Answer 1

The average rate of change of the function f(x) = 6x^3 from x1 = 5 to x2 = 10 is 1050.

Step-by-step explanation:

The average rate of change of the function f(x) = 6x^3 from x1 = 5 to x2 = 10 is calculated using the formula:

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1).

First, we'll find the values of f(x1) and f(x2):

• f(5) = 6(5)^3 = 6(125) = 750
• f(10) = 6(10)^3 = 6(1000) = 6000

Next, we substitute these values into the formula:

Average Rate of Change = (6000 - 750) / (10 - 5) = 5250 / 5 = 1050

Therefore, the average rate of change is 1050.