Maxima & Minima Class 12 🔥 Second Derivative Test | Word Problems | NCERT Ch-6 | Faiz Sir

📘 Application of Derivatives – Class 12 Maths | Chapter 6 (NCERT)
🎯 Topic: Maxima & Minima – Second Derivative Test + Advanced Word Problems
👨‍🏫 By: Faiz Sir | Infinix Classes

इस वीडियो में हम Class 12 Maths – Application of Derivatives (Chapter 6) के Maxima and Minima टॉपिक का Second Derivative Test detail में पढ़ेंगे और NCERT के advanced level word problems step-by-step solve करेंगे।

🔹 इस वीडियो में आप सीखेंगे:

✔ Second Derivative Test (Theorem 4) – पूरा concept
✔ Local Maxima & Local Minima की पहचान
✔ f′(c) = 0 और f″(c) का use
✔ जब Second Derivative Test fail हो जाए
✔ Real life & word problems from NCERT

📌 NCERT Examples Covered:

📍 Example 19 – |x| function का local minimum
📍 Example 20 – Polynomial function (Max & Min)
📍 Example 21 – Cubic function analysis
📍 Example 22 – Numbers whose sum of squares is minimum
📍 Example 23 – Shortest distance problem
📍 Example 24 – Minimum distance between poles
📍 Example 25 – Maximum area of trapezium
📍 Example 26 – Maximum curved surface area of cylinder in cone

👉 यह वीडियो Board Exam, CBSE, NCERT, JEE foundation और concept clarity के लिए बेहद important है।
📈 अगर आप Maxima Minima numerical, word problems और derivative tests में strong होना चाहते हैं, तो यह lecture जरूर देखें।

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Example 22: Find two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Example 23: Find the shortest distance of the point (0, c) from the parabola y = x2, where 𝟏/𝟐 ≤𝒄≤𝟓.



Example 24: Let AP and BQ be two vertical poles at points A and B, respectively. If AP = 16 m, BQ = 22 m and AB = 20 m, then find the distance of a point R on AB from the point A such that RP2 + RQ2 is minimum.

Example 25: If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.


Example 26: Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.