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Question #40529

Difficulty: 8/10 | 🟢 Free

The Question

Let $f(x) = \frac{|x^2 - 34x + 271|}{x^2 - 34x + 245}$ . Let $S_1$ be the sum of all $x$ where $f(x)$ attains a local maximum, and $S_2$ be the sum of all $x$ where $f(x)$ attains a local minimum. If $f(x)$ is non-differentiable at exactly $k$ points in its domain, find the value of $S_1 - S_2 + k$ .

Options

A.
17
B.
19
C.
21
D.
36

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Denominator Restriction|Completing the Square in Quadratics|Modulus Function Breakdown|Non-Differentiable Extrema

Why This Question Is Tricky

Common Mistakes

This question tests the 'Modulus Breakdown' and 'Denominator Restriction' traps.

Students often mechanically differentiate to find extrema, incorrectly assuming $f'(x) = 0$ is a necessary condition, thereby missing the non-differentiable local maxima (cusps) at the roots of the modulus argument.

Furthermore, the denominator restriction creates vertical asymptotes; a common trap is counting these asymptotes as points of non-differentiability, failing to realize they are excluded from the function's domain.

The constants 245 and 271 are specifically chosen to force a domain analysis where the modulus roots lie strictly between the local minimum and the asymptotes.

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