#math

Explain the real-world application of derivatives. Concept: Rate of change. Examples: 1. Speedometer (Position vs Time). 2. Marginal cost in economics. 3. Optimization (Finding max/min). Avoid complex formulas, focus on intuition.

Scale recipes accurately for catering. Scaling factor: desired servings ÷ original servings. Multiply all ingredients by factor. Challenges: 1. Spices scale at 50-75% (not linear). 2. Thickeners (flour, cornstarch) at 80%. 3. Leavening agents carefully. 4. Salt to taste. 5. Cooking time: doesn't double with quantity. Equipment limits: oven capacity, mixing bowl size. Test small batch first. Baker's percentage for bread: all ingredients as % of flour weight. Explain why some ingredients don't scale linearly and surface area vs volume ratio.