Don't Get Trapped by [4x]! Mastering Continuity & Differentiability | JEE Advanced (Day 09/90)

Описание: Day 09 of our 90-Day Challenge features a multi-concept problem from JEE Advanced (2023 Paper 2 Q6) involving the Greatest Integer Function $[x]$ and its impact on differentiability. Students often miss the critical points where the polynomial parts "save" the function from jumps.
In this Masterclass, we analyze:

Critical Points of $[4x]$:
Identifying the potential jump points at $x = \frac{1}{4}, \frac{1}{2}, \frac{3}{4}$.
The "Zero-Power" Rule: How $(x - \frac{1}{4})^2$ and $(x - \frac{1}{2})$ dictate continuity and differentiability at the boundaries.
Finding the Global Minimum: Calculating the vertex of the quadratic portion to verify the minimum value.
Option Elimination: Proving why Statement (B) is the subtle trap of this entire question.

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