1. What is Net Change?

The net change of a function between two points represents the overall difference in the function's value from the starting point to the ending point. It's calculated as the difference between the function's value at the end point and its value at the starting point.

2. How Does the Calculator Work?

The calculator uses the net change formula:

Where:

• \( f \) — The function being evaluated
• \( a \) — The starting point
• \( b \) — The ending point

Explanation: The calculator evaluates the function at both points and subtracts the starting value from the ending value to determine the net change.

3. Importance of Net Change

Details: Net change is fundamental in calculus and real-world applications. It's used to calculate total change in quantities like distance, population, temperature, or stock prices over time.

4. Using the Calculator

Tips:

• Enter the function using standard mathematical notation (e.g., "x^2 + 3*x - 5")
• Use 'x' as the variable in your function
• For exponents, use either '^' or '**' (e.g., "x^2" or "x**2")
• Start and end points can be any real numbers

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between net change and average rate of change?
A: Net change gives the total difference (f(b)-f(a)), while average rate of change gives the difference per unit (f(b)-f(a))/(b-a).

Q2: Can I use trigonometric functions?
A: This basic calculator supports simple algebraic expressions. For advanced functions, you'd need a more sophisticated evaluator.

Q3: What if my function isn't continuous between a and b?
A: The net change still calculates the difference in endpoint values, but may not represent the actual change that occurred between them.

Q4: How is net change related to integrals?
A: For continuous functions, the net change equals the definite integral of the derivative over the interval.

Q5: Can I calculate net change for non-mathematical functions?
A: The concept applies to any measurable quantity, but this calculator only handles mathematical functions.