L.C. Maths H.L. 2025 Q3 (b): PROOF NO Max/Min Points (Calculus)

Описание: 🔥 Leaving Cert Maths Higher Level Revision: NO Local Max/Min Points 🔥

This video solves **Question 3 (b) from the LCHL 2025 Paper 1**, showing you how to PROVE a function has no turning points. This is a common and tricky style of question!

*In this tutorial, you will master:*
1. *Derivatives of Fractions:* Converting the function (g(x) = 3 / (2x - 7)) to a negative power (Chain Rule method) for differentiation.
2. The fundamental rule for finding turning points: setting the **First Derivative equal to Zero (g'(x) = 0)**.
3. The crucial *Final Proof* that results in the statement "–6 ≠ 0," confirming **NO Local Maximum or Minimum Points**.
4. Full steps for an **H1**-standard answer.

This is essential *Calculus* practice for showing higher-level comprehension in your Leaving Cert exam!

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0:00 Intro & Proof: No Max/Min Points Sets the stage and confirms the problem type.
1:02 The 4 Steps to Finding Max/Min Points A quick conceptual roadmap for students.
2:12 Step 1: Converting to a Negative Power (Differentiation Setup) The essential first step for your preferred method.
3:17 Step 2: Applying the Chain Rule to find g'(x) The core differentiation process.
4:09 The Full Derivative g'(x) Calculated The final result of the differentiation.
5:26 Step 3: Setting the Derivative to Zero (g'(x) = 0) The crucial step for finding turning points.
5:57 The Final PROOF: Why –6 ≠ 0 (No Solution) The conceptual conclusion that answers the exam question.