Introducción al Cálculo Diferencial
Introducción a los conceptos fundamentales del cálculo diferencial
Interactive Differential Calculus Visualization
Welcome to the Differential Calculus Explorer
This interactive visualization helps you understand the fundamental concepts of differential calculus: derivatives, tangent lines, and secant lines. Explore how secant lines approach tangent lines as the distance between points approaches zero, which is the core idea behind derivatives.
What you can explore:
- Polynomial functions - Learn with f(x) = x² and see how derivatives work
- Trigonometric functions - Explore f(x) = sin(x) and its derivative
- Exponential functions - Discover f(x) = e^x and its unique property
- Rational functions - Understand f(x) = 1/x and its derivative
How to Use This Visualization
Interactive Features:
- • Select Function Type - Choose from 4 different functions to explore
- • Adjust Point x - Use the slider or click on the graph to set the point
- • Adjust Distance h - Control the distance between two points on the curve
- • Toggle Visualizations - Show/hide secant line, tangent line, and derivative value
- • Animate h → 0 - Watch the secant line approach the tangent line
What You'll See:
- • Function Curve (solid, colored) - The original function f(x)
- • Secant Line (purple, dashed) - Line connecting two points on the curve
- • Tangent Line (red) - Line that touches the curve at exactly one point
- • Main Point (colored circle) - The point where the tangent is drawn
- • Second Point (purple circle) - The second point forming the secant line
- • Derivative Value - Real-time display of f'(x) at the selected point
- • Calculation Steps - Step-by-step breakdown of the derivative calculation
Click on the graph to move the point
As h → 0, secant line approaches tangent line
Current Values
Point: (1.000, 1.000)
Second Point: (2.000, 4.000)
Secant Slope: 3.0000
Tangent Slope (f'): 2.0000
Key Concepts
Derivative: The slope of the tangent line at a point represents the instantaneous rate of change.
Secant Line: A line connecting two points on the curve. As the distance h approaches 0, the secant line approaches the tangent line.
Tangent Line: A line that touches the curve at exactly one point, representing the derivative.
Derivative Definition
f'(x) = limh→0 [f(x+h) - f(x)] / h
The derivative is the limit of the difference quotient as h approaches zero. This is what we visualize when the secant line approaches the tangent line.
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