G06 // Cartesian Plane & Functions
Geometric Meaning of the Derivative: Tangent Line, Secant & Non-Differentiable Points
Vector construction of the difference quotient Δy/Δx, secant-to-tangent limit at x₀, derivative curve f'(x), and singular points (cusps, corners, vertical tangents).
Key formulas & geometric relations
f'(x₀) = lim_{h→0} [f(x₀ + h) − f(x₀)] / h · y − f(x₀) = f'(x₀) · (x − x₀) · m_sec = Δy / Δx