Question

Find the average rate of change of f(x)=3x²−2x from 1 to 2?

Answer 1

The average rate of change of the function f(x) = 3x² − 2x from x = 1 to x = 2 is found to be 7 by evaluating the function at the given points and applying the average rate of change formula.

Step-by-step explanation:

To find the average rate of change of the function f(x) = 3x² − 2x from x = 1 to x = 2, you need to use the formula:

Average Rate of Change = ∆f(x) / ∆x = [f(x2) - f(x1)] / [x2 - x1]

Let's calculate it step by step:

1. First, plug in the values into the function to get f(1) and f(2):

• f(1) = 3(1)² − 2(1) = 3 − 2 = 1
• f(2) = 3(2)² − 2(2) = 12 − 4 = 8

Next, subtract f(1) from f(2) and divide by the change in x (2 - 1):

• Average Rate of Change = (8 − 1) / (2 - 1) = 7 / 1 = 7

Therefore, the average rate of change of f(x) from 1 to 2 is 7.