Instantaneous Rate of Change Calculator

A Python project that generates random polynomial curves and calculates the instantaneous rate of change at any point using derivatives and tangent lines.

Overview

This program:

1. Generates a random polynomial equation
2. Finds the tangent line at a specific point
3. Calculates the instantaneous rate of change (derivative) at that point
4. Displays polynomial graph, tangent line graph, then both graphs together

Requirements

Start an virtual environment:

https://docs.python.org/3/library/venv.html

pip install sympy matplotlib

Usage

Run the main program:

python main.py

Example Output

[-3.7482081877974673, -4.5016147894208345, 4.166184518768379] # Random coefficients
-3.75*x**2 - 4.50*x + 4.17                                    # Polynomial equation
379.17 - 79.5*x                                               # Tangent line at x=10
-415.83                                                       # Value at x=10

1. polynomial graph

2. tangent line graph

3. both graphs combined

How It Works

The program uses calculus concepts:

• Derivative: The rate of change of the polynomial
• Tangent Line: A line that touches the curve at exactly one point
• Instantaneous Rate: The slope of the tangent line (derivative value)