Average Rate of Change Calculator

This average rate of change calculator finds the slope of your function over an interval.

It also plots the function and the secant line.

You see numbers and a clear graph in one place.

Why Use Our Average Rate of Change Calculator?

This tool gives quick answers and a visual check.

It works with many functions and shows each step.

It helps you check work and build strong intuition.

How It Works

The average rate of change from a to b equals the secant slope.

Average rate of change equals f(b) minus f(a), divided by b minus a.

The calculator evaluates f at both x values and shows each number.

It draws the curve and the two points.

It also draws the secant line through them.

How to Use This Tool

1. Enter your function in the f(x) field. Use x as the only variable.
2. Use plus and minus. Use multiply and divide. Use the caret for powers.
3. You can use sin and cos. You can use tan and sqrt. You can use abs. You can use log and ln. Log means base 10. Ln means natural log. You can use exp for the exponential function. You can use pi and e as constants.
4. Enter the initial x value a.
5. Enter the final x value b.
6. Click Calculate to run the math. You can press Enter in any field.

Here is what each field expects.

• Function f(x): Type your expression with x. Write 2*x to multiply. Use parentheses to control order. Angles use radians for trig functions.
• Initial x value a: Set the start of the interval. You can use decimals.
• Final x value b: Set the end of the interval. You can use decimals.

Here is how to read the results.

• Function shows the exact text you entered.
• Point 1 shows f(a) and its value.
• Point 2 shows f(b) and its value.
• The calculator prints the formula with your numbers.
• The final slope appears with four decimal places.
• The graph shows the curve and the two points.
• It also shows the secant line across the interval.

Notes and limits.

• Use different start and end x values.
• Choose x values that keep the function defined.
• For sqrt(x), pick x at least zero.
• For log(x) or ln(x), pick x greater than zero.
• For tan(x), pick x away from pi over two values.
• Write 2*x for products.
• The text output rounds to four decimals.
• The graph window centers on your interval with a small margin.
• Very steep functions may exceed the view.

Common use cases.

• Algebra practice for slope across an interval.
• Precalculus work with secant lines.
• Early calculus to compare with a derivative at a point.
• Physics to find average velocity from a position function.
• Business to gauge average change in a model.

Quick examples.

• For f(x)=x^2 on 1 to 3, the slope equals 4.
• For f(x)=2*x+3 on 0 to 5, the slope equals 2.
• For f(x)=sin(x) on 0 to pi, the slope equals 0.

Benefits at a Glance

• Clear math steps and a helpful graph.
• Works with common functions and constants.
• Good for quick checks in class or work.

Enter a function and two x values.

Review the steps and the graph.

Build a clear grasp of the concept.