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Applications of Derivatives formula sheet
All 15 Applications of Derivatives formulas in CalcRef on one printable page, each with its conditions. Tangent lines, optimization, related rates, and curve sketching.
Applications of Derivatives| Formula | Statement | Conditions |
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| Tangent Line | y−f(a)=f′(a)(x−a) | no restriction stated |
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| Normal Line | y−f(a)=−f′(a)1(x−a) | f'(a) ≠ 0. |
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| Critical Points | f′(c)=0 or f′(c) DNE⇒c is a critical point | no restriction stated |
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| First Derivative Test | f′ changes +→−⇒local max;f′ changes −→+⇒local min | no restriction stated |
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| Second Derivative Test | f′(c)=0:f′′(c)>0⇒local min;f′′(c)<0⇒local max | no restriction stated |
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| Concavity | f′′(x)>0⇒concave up;f′′(x)<0⇒concave down | no restriction stated |
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The 15 Applications of Derivatives formulas in the CalcRef library, every one of them free to read at /topics/applications-derivatives.
CalcRef is an educational reference. Check every statement on this sheet against your own course notes, textbook or exam formula policy before relying on it in graded work.