← CBSE Class 12
Applications of Derivatives
Chapter Overview
Rate of change dy/dx describes how y changes with x. Increasing/decreasing functions: f'(x) > 0 means increasing, f'(x) < 0 means decreasing at a point. Tangents and normals use the derivative as slope. Maxima and minima: critical points where f'(x) = 0, second derivative test for determining max/min. Optimization problems find extreme values given constraints.
Topics Covered
- Rate of Change
- Increasing and Decreasing Functions
- Tangents and Normals
- Approximations
- Maxima and Minima
- First Derivative Test
- Second Derivative Test
- Optimization Problems
Key Formulas
f'(x) > 0 => increasing
f'(x) < 0 => decreasing
Tangent: y - y1 = f'(x1)(x - x1)
Max: f''(x) < 0
Min: f''(x) > 0
Real-World Applications
Applications: Profit maximization, package design, engineering optimization, physics problems.
Study Tips
Tip: Set derivative = 0 to find critical points
Tip: Use second derivative test to classify
Tip: Draw sign diagrams for intervals