Geometric Meaning of the Derivative

Secant & Tangent Line Limit Visualization

Function f(x) = x³ - 3x

Derivative f'(x) = 3x² - 3

Preset Function

Base Point $x_0$: 0.80

Step Size $h$: 1.50

Point A ($x_0, f(x_0)$): (0.80, -2.25)

Point B ($x_0+h, f(x_0+h)$): (2.30, 5.27)

Run ($\Delta x = h$)

1.500

Rise ($\Delta y$)

7.520

Secant Slope ($\frac{\Delta y}{\Delta x}$)

5.013

Tangent Slope ($f'(x_0)$)

-1.080