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Question #40538

Difficulty: 8/10 | 🟢 Free

The Question

Let $f: \mathbb{R} \setminus \{-2, 2\} \to \mathbb{R}$ be defined as $f(x) = \frac{|x^2 - 1| - 2}{x^2 - 4}$ If $S$ is the set of all points of local extrema of $f$ , then the value of $\sum_{x \in S} (x^2 + 2)$ is:

Options

A.
6
B.
8
C.
20
D.
2

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Monster

Ultra-high difficulty questions designed to test your limit, stamina, and deep conceptual understanding.

Concepts Behind This Question

Denominator Restriction|Non-Differentiable Extrema|Modulus Function Symmetry

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between true critical points (where the function is defined but non-differentiable, such as cusps) and domain restrictions (vertical asymptotes).

A common trap is blindly finding where the derivative's denominator is zero, leading students to incorrectly include $x = \pm 2$ as local extrema (yielding the trap answer 20).

Furthermore, students might miss the cusps at $x = \pm 1$ if they only solve $f'(x) = 0$ , testing their rigor in handling modulus functions within quotients.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Linear Inequalities - Class 11
Concept	Denominator Restriction
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free