Problems Solving - Increasing & Decreasing Functions | Class 12, JEE Maths | Rohit Ranjan (IIT KGP)

Increasing & Decreasing Functions | Problem Solving | Application of Derivatives | Class 12 In this video, we solve exam-oriented problems based on increasing and decreasing functions, using the concept of monotonicity and first derivatives from the chapter Application of Derivatives. The focus is on step-by-step problem solving, showing how to analyze the sign of the derivative to determine whether a function is strictly increasing or strictly decreasing over given intervals. 🔹 Problem 1 For the function f(x) = x⁴/4 − x³ − 5x² + 24x + 12 Find the intervals in which the function is: Strictly increasing Strictly decreasing 📌 Concepts applied: First derivative of a polynomial function Finding critical points Sign analysis of f′(x) Determining monotonic intervals ✔ This problem strengthens understanding of interval-based questions frequently asked in board exams. 🔹 Problem 2 Prove that the function f(x) = log(1 + x) − (2x / (x + 2)) is an increasing function for x greater than −1 📌 Concepts applied: Differentiation of logarithmic and rational functions Simplifying f′(x) Showing f′(x) greater than 0 for a given domain Using derivatives to prove monotonicity ✔ This is a proof-based question, very important for CBSE board exams. 🔹 What You Will Learn ✔ How to find intervals of increase and decrease ✔ Difference between increasing and strictly increasing ✔ How to justify monotonicity using derivatives ✔ Handling polynomial and logarithmic functions ✔ Writing proper board-exam standard solutions 🔹 Why This Video Is Important ✔ Covers high-probability board questions ✔ Builds confidence in derivative-based analysis ✔ Improves clarity for both numerical and proof-based problems This video is part of the Application of Derivatives playlist for Class 12 Mathematics. increasing and decreasing functions class 12, monotonicity problems class 12, application of derivatives problem solving, strictly increasing function, strictly decreasing function, cbse class 12 maths calculus, derivative sign method, polynomial function monotonicity, log function increasing decreasing, board exam calculus questions