Left - hand and Right - hand Derivatives
The left - hand derivative of a function f(x) at a point x₀: f'₋(x₀) = lim(Δ x → 0⁻) (f(x₀ + Δ x) - f(x₀))/(Δ x). The right - hand derivative: f'₊(x₀) = lim(Δ…
Syllabus path: Functions › Preliminary Derivatives › Definition of the Derivative
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CSCA Mathematics Formula Reference
Formula and explanation
The left - hand derivative of a function f(x) at a point x₀: f'₋(x₀) = lim(Δ x → 0⁻) (f(x₀ + Δ x) - f(x₀))/(Δ x). The right - hand derivative: f'₊(x₀) = lim(Δ x → 0⁺) (f(x₀ + Δ x) - f(x₀))/(Δ x). Condition: For piecewise functions at breakpoints or endpoints of intervals. A function is differentiable at a point if and only if both the left - hand and right - hand derivatives exist and are equal.
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Definition of the Derivative
Definition of the Derivative 1. Core Concepts The Derivative is the cornerstone of calculus, quantifying how fast a function changes at a specific point. Physical Meaning: Instantaneous Rate of Change (e.g., Velocity is the derivative of Displacement). Geometric Meaning: The Slop…
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