Zoom Into the Curve
Drag a point along any function, see the tangent line and slope, then zoom in to watch the curve become locally linear — an interactive introduction to derivatives.
Frequently Asked Questions
What is a derivative?
A derivative measures how fast a function is changing at any point. Geometrically, it is the slope of the tangent line to the curve at that point. If f(x) = x², the derivative f'(x) = 2x tells you the slope doubles as x doubles.
Why does the curve look like a straight line when you zoom in?
Smooth functions are "locally linear" — if you zoom in far enough around any point, the curve becomes indistinguishable from its tangent line. This is the fundamental idea behind differential calculus.
How is the derivative calculated here?
The tool uses the central difference formula: f'(x) ≈ (f(x+h) − f(x−h)) / (2h) with a very small h = 0.0001. This numerical approximation is accurate to about 8 decimal places for smooth functions.
Can I enter my own function?
Yes! Click "Custom" and type any expression using x, numbers, +, -, *, ^, sin(), cos(), and parentheses. For example: x^3 - 3*x, sin(x)*x, or 2*x^2 + 1.
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