Application of Derivatives: One-Page Formula Sheet

Application of Derivatives — formula sheet

Formulas

• Tangent: y − y₁ = m(x − x₁), m = f′(x₁)
• Normal slope = −1/m
• LMVT: f′(c) = (f(b) − f(a))/(b − a)
• Second derivative test: f″(c) < 0 → max

Key ideas

• f′(x) > 0 means increasing
• At a local max f′ = 0 and f″ < 0
• Check endpoints for absolute max/min on a closed interval
• Rolle's and Lagrange's mean value theorems

Traps to avoid

• Forgetting endpoints
• Using f′ = 0 points without checking sign change
• Sign errors in normal slope

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