Calculus Revisited: Herb Gross Chalkboard

Unit 1: Analytic Geometry, Secants & Instantaneous Derivative Limits
Chalkboard Parameters
Calculus Evidence
f(x) at x: -2.000
Secant Slope [Δy/Δx]: 0.250
Tangent Slope f'(x): 0.000
Local Linearity: 98.0%
Differentiability: DIFFABLE
Herb Gross Insight
"As Δx approaches zero, the secant chord rotates continuously into the tangent vector. Under continuous magnification, smooth curvature vanishes into a straight line."
Drag point P(x) directly on chalkboard | Dual Pane: f(x) Left & Derivative f'(x) Right
Analytic Geometry Proof: f(x) = x³ - 3x
lim_{Δx → 0} [f(x + Δx) - f(x)] / Δx = f'(x) = 3x² - 3

At x = 1.00, f(1.00) = -2.000. As interval Δx shrinks from 0.50 down to 0, the secant line slope converges dynamically to the exact derivative value 0.000.