What is how to find average rate of change?

Here's how to find the average rate of change:

The average rate of change of a function f(x) between two points x = a and x = b is a measure of how much the function's output changes per unit change in its input over that interval. It's essentially the slope of the secant line connecting the two points (a, f(a)) and (b, f(b)) on the graph of the function.

Formula:

The average rate of change is calculated using the following formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

Where:

• f(b) is the value of the function at x = b.
• f(a) is the value of the function at x = a.
• b - a is the change in the x-value (the interval).

Steps to Calculate the Average Rate of Change:

1. Identify the interval: Determine the values of a and b for the interval you're interested in.
2. Evaluate the function: Calculate f(a) and f(b). This means plugging the values of a and b into the function f(x).
3. Apply the formula: Substitute the values you found in steps 1 and 2 into the average rate of change formula: (f(b) - f(a)) / (b - a)
4. Simplify: Simplify the expression to obtain the average rate of change. The result will be a numerical value representing the rate of change over the specified interval.

Example:

Let's say we have the function f(x) = x² and we want to find the average rate of change between x = 1 and x = 3.

1. a = 1, b = 3
2. f(1) = 1² = 1 f(3) = 3² = 9
3. Average Rate of Change = (9 - 1) / (3 - 1)
4. Average Rate of Change = 8 / 2 = 4

Therefore, the average rate of change of f(x) = x² between x = 1 and x = 3 is 4.

Important Concepts:

• Function
• Slope
• Interval
• Secant%20Line