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Applications of derivatives formulas
11 formulas for Applications of derivatives, from the Calculus section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Slope of tangent | m = dy/dx at (x₁, y₁) | |
| Tangent line | y − y₁ = m(x − x₁) 🧮 Solve step by step | |
| Normal line | y − y₁ = −(1/m)(x − x₁) 🧮 Solve step by step | |
| Increasing / decreasing | f′(x) > 0 increasing; f′(x) < 0 decreasing | |
| Critical point | f′(x) = 0 or undefined | |
| Second derivative test | f″ < 0 maximum; f″ > 0 minimum | |
| Point of inflection | f″ changes sign | |
| Rate of change | dA/dt = (dA/dr)(dr/dt) | |
| Approximation | f(x + Δx) ≈ f(x) + f′(x)Δx | |
| Mean value theorem | f′(c) = (f(b) − f(a))/(b − a) | |
| Taylor series | f(x) = Σ f⁽ⁿ⁾(a)(x − a)ⁿ / n! |
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