1. What is Net Change?

The net change of a function between two points represents the difference in the function's output values at those points. Mathematically, it's expressed as f(b) - f(a), where f is the function, and a and b are the input values.

2. How Does the Calculator Work?

The calculator uses the net change equation:

Where:

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

Explanation: The net change measures how much the function's output changes between point a and point b.

3. Importance of Net Change

Details: Net change is fundamental in calculus and real-world applications. It helps quantify differences in quantities like position, temperature, or stock prices over intervals.

4. Using the Calculator

Tips: Enter a valid mathematical function (e.g., "x^2", "sin(x)", "2*x+3"), and the start and end points. The calculator will evaluate the function at both points and compute the difference.

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 is (f(b)-f(a))/(b-a), representing the slope between points.

Q2: Can net change be negative?
A: Yes, if f(b) < f(a), the net change will be negative, indicating a decrease in the function's value.

Q3: What functions can I enter?
A: The calculator supports basic arithmetic, exponents, and common functions like sin, cos, log, etc. (implementation dependent).

Q4: How is this related to integrals?
A: The net change is equivalent to the definite integral of the derivative of f from a to b (Fundamental Theorem of Calculus).

Q5: What if my function isn't continuous?
A: The net change still applies, but be aware of discontinuities between a and b that might affect interpretation.