Math Problem Statement

Use the table below to find the average rate of change between x=2 and x=5.

Solution

To find the average rate of change of a function between two points x=2x = 2 and x=5x = 5, we use the formula for the average rate of change:

Average rate of change=f(x2)f(x1)x2x1\text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

Where:

  • x1=2x_1 = 2
  • x2=5x_2 = 5
  • f(x1)f(x_1) is the value of the function at x1=2x_1 = 2
  • f(x2)f(x_2) is the value of the function at x2=5x_2 = 5

You need to provide the table with the function values so I can substitute these values into the formula and calculate the average rate of change. Could you share the table?

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Math Problem Analysis

Mathematical Concepts

Calculus
Rate of Change
Linear Approximation

Formulas

Average rate of change formula: (f(x2) - f(x1)) / (x2 - x1)

Theorems

Slope of the secant line between two points on a function

Suitable Grade Level

Grades 9-12