Advanced Derivatives - Tangent Line Animation

The derivative of a function at a given point is the rate of change of the function's value at that point. It is often interpreted as the slope of the tangent line at that point. Mathematically, the derivative is the limit of the difference quotient as the interval approaches zero.

Key Concepts:

The derivative represents the slope of the tangent line to the curve at a given point.
Instantaneous rate of change refers to the rate at which the function is changing at any given moment.
Mathematically, the derivative of a function f(x) at a point x=a is given by:

f'(a) = lim (h -> 0) [f(a + h) - f(a)] / h

Function (f(x)): x² Point (x): 0 Zoom Level:

Real-Time Data: Slope of Tangent (f'(x)): -- Derivative (f'(x)) Function: --

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