Exercise 2.9 Class 12 maths || NBF 2025 New Book || ex 2.9 NBF Class 12 maths || By Sir Raaz

Exercise 2.9 – 2nd Year Math | Critical Points, Extrema, Concavity, Inflection Points | Full Solution in Urdu

Welcome to a complete and detailed explanation of Exercise 2.9 from Grade 12 (FSc Part 2) Mathematics. This video provides a step-by-step solution to problems involving critical points, maximum/minimum values, concavity, and points of inflection using first and second derivative tests.

✅ Find Critical Values of Functions
✅ Absolute & Relative Extrema (Maximum & Minimum)
✅ Use of Second Derivative for Concavity
✅ Points of Inflection
✅ Solve using First Principles and Graphical Insight
✅ Functions involving Polynomial, Trigonometric, Rational, Exponential forms

📘 This video is ideal for students preparing for board exams (Punjab/FBISE) and entry tests (ECAT/MDCAT). The explanation is in simple Urdu/Hindi, perfect for FSc and ICS students.
Topics Covered:

First Derivative Test

Second Derivative Test

Absolute Extrema on Closed Intervals

Concave Up/Down Analysis

Inflection Points

Optimization Techniques
Perfect For:

FSc Part 2 / Class 12 Math Students

ICS / Pre-Engineering / Pre-Medical Students

Board Exam Preparation (Punjab, Federal, Sindh)

ECAT / MDCAT / University Entry Tests
CHAPTERS:
00:00 Intro
00:25 Q#1 (i)
03:15 Q#1 (ii)
05:32 Q#1(iii)
07:38 Q#1(iv)
12:00 Q#1(v)
15:35 Q#1(vi)
19:12 Q#2(i)
23:36 Q#2(ii)
26:15 Q#2(iii)
30:05 Q#2(iv)
33:42 Q#2(v)
36:33 Q#2(vi)
42:45 Understanding Concavity
44:02 Q#3(i)
45:07 Q#3(ii)
48:15 Q#3(iii)
52:10 Q#3(iv)
59:45 Q#3(v)
01:03:07 Q#3(vi)
01:05:29 Q#4(i)
01:09:01 Q#4(ii)
01:10:15 Q#4(iii)
01:12:55 Q#4(iv)
1:16:27 Q#4(v)
01:18:19 Q#4(vi)
01:20:57 Understanding Local Maximum And Local Minimum
01:23:04 Q#5(i)
01:26:10 Q#5(ii)
01:28:38 Q#5(iii)
01:31:57 Q#5(v)
01:38:31 Q#5(vi)
01:43:39 Understanding Relative Maximum and Relative Minimum
01:44:24 Q#6(i)
01:47:14 Q#6(ii)
01:48:04 Q#6(iii)
01:51:10 Q#6(iv)

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Видео Exercise 2.9 Class 12 maths || NBF 2025 New Book || ex 2.9 NBF Class 12 maths || By Sir Raaz канала Maths Ka Raaz