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Question #41341

Difficulty: 8/10 | 🟢 Free

The Question

Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = 15x^7 - 140x^6 + 504x^5 - 840x^4 + 560x^3 + 59$ . Let $g(x)$ be the inverse function of $f(x)$ . If $S$ is the set of all real numbers $y$ such that $g$ is not differentiable at $y$ , then the sum of all elements in $S$ is

Options

A.
246
B.
187
C.
128
D.
59

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

Inverse Function Derivative|Critical Point vs Stationary Point|Second Derivative Test Limitations|Even Multiplicity Roots

Why This Question Is Tricky

Common Mistakes

This question tests the differentiability of inverse functions at points corresponding to stationary points of the original function.

The trap lies in the 'Even Multiplicity Roots' of the derivative; students often assume $f'(x)=0$ implies local extrema, failing to recognize that even multiplicity roots create inflection points where the function remains strictly monotonic and invertible.

Consequently, they might incorrectly conclude the inverse doesn't exist or miss the division-by-zero singularity in $(f^{-1})'(y) = 1/f'(x)$ , which precisely identifies the points of non-differentiability.

The integration trick avoids brutal polynomial evaluation, rewarding algebraic foresight.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Continuity and Differentiability - Class 12
Concept	Inverse Function Derivative
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free