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Question #60796
The Question
Consider the function . \ \textbf{Statement I:} There does not exist any such that . \ \textbf{Statement II:} Rolle's Theorem is not applicable to on the interval because is non-differentiable at .
Options
- A.
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
- B.
Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I
- C.
Statement I is true, Statement II is false
- D.
Statement I is false, Statement II is true
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
Properties of Arithmetic Mean|Mean Value Theorem Applicability|Modulus Function Breakdown
Why This Question Is Tricky
Examiner Levers
Logical Assertion
Tests the causal relationship between two true statements.
Difficulty Boost : +4Common Mistakes
This question tests the causal relationship between the non-applicability of Rolle's Theorem and the non-existence of a zero derivative.
The 'Modulus Function Breakdown' creates multiple non-differentiable points, making Statement II true.
Students often fall into the trap of assuming that because the theorem's prerequisites fail, the conclusion must also fail, thereby incorrectly choosing Statement II as the explanation for Statement I.
However, the true reason is the parity of the number of terms in the arithmetic mean of the modulus functions; an even number of terms would yield a zero derivative interval despite the exact same non-differentiability conditions.
Quick Facts About This Question
Question Information
| Subject | Mathematics |
| Chapter | Statistics - Class 11 |
| Concept | Properties of Arithmetic Mean |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |