Application of Derivatives

🏫 MP BoardClass 12Mathematics

💡 Application of Derivatives: Key Concepts

Derivatives measure how one quantity changes relative to another. Key applications include: • Rate of Change: dy/dx represents instantaneous change. • Increasing/Decreasing Functions: f'(x) > 0 means increasing; f'(x) < 0 means decreasing. • Maxima and Minima: Critical points occur where f'(x) = 0, helping find maximum or minimum values.

💡 Increasing and Decreasing Functions

A function f(x) is increasing on an interval if its derivative f'(x) > 0, and decreasing if f'(x) < 0.

Key Rules: • Strictly Increasing: f'(x) > 0 • Strictly Decreasing: f'(x) < 0 • Constant: f'(x) = 0

Steps:

  1. Find derivative f'(x).
  2. Solve f'(x) = 0 to get critical points.
  3. Check the sign of f'(x) in each interval.