Uploaded August 2026 | Updated September 2026, 2 weeks ago

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Can you find the minimum value of

(x² + 6x + 13)/(x + 3), where x is more than 0?

At first, this looks like a straightforward AM-GM problem. Rewrite the expression, apply AM-GM, and you seem to get an answer immediately.

But there is a catch.

The equality condition given by AM-GM must also satisfy the DOMAIN of the original function.

In Visual Maths Lab 019, we explore this question visually using algebra, domain restrictions and the graph of the transformed function.

This is an important idea for CAT Quant:
A lower bound and an attainable minimum are NOT always the same thing.

Can you identify the trap before watching the complete solution?

Topics:
CAT Quant
Algebra
Functions
AM-GM Inequality
Domain and Range
Minimum Value
Infimum
Graph-Based Mathematics

Think CAT • Think AzuCATion

When it’s Maths, it must be Maths By Amiya.

#CAT2026 #CATQuant #QuantitativeAptitude #Algebra #Functions #AMGM #Mathematics #CATPreparation #VisualMathsLab #AzuCATion