1. What is Instantaneous Rate of Change?

The instantaneous rate of change (IROC) at a point is the slope of the tangent line to the function's curve at that point. Mathematically, it's the value of the derivative f'(x) at a specific x value.

2. How Does the Calculator Work?

The calculator uses the derivative function:

Where:

• \( f'(x) \) — Derivative of the original function
• \( x \) — The specific point where IROC is calculated

Explanation: The calculator evaluates the derivative function at the given x value to find the slope of the tangent line at that point.

3. Importance of IROC Calculation

Details: IROC is fundamental in calculus and physics, representing quantities like velocity (derivative of position), acceleration (derivative of velocity), and marginal cost in economics.

4. Using the Calculator

Tips: Enter the derivative function using standard mathematical notation (e.g., "3x^2 + 2x" for 3x² + 2x) and the x value where you want to find the rate of change.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and instantaneous rate of change?
A: Average rate is over an interval (Δy/Δx), while instantaneous is at a single point (the derivative).

Q2: Can I enter trigonometric functions?
A: This simplified version handles polynomials. For full functionality, you'd need a more advanced parser.

Q3: What if I get an error message?
A: Check your derivative expression for proper syntax. Use "x" as the variable and "^" for exponents.

Q4: How accurate is this calculator?
A: For simple polynomials, it's exact. For complex functions, consider specialized math software.

Q5: What are common applications of IROC?
A: Physics (motion analysis), economics (marginal analysis), biology (growth rates), and engineering.