Assertion : If g (x) is a differentiable function g (1) ≠ 0, g (–1) ≠ 0 and Rolles…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Assertion : If g (x) is a differentiable function g(1) ≠ 0,
g (–1) ≠ 0 and Rolles theorem is not applicable to \(f(x)=\frac{x^{2}-1}{g(x)}\) in [–1, 1], then g(x) has atleast one root
in (–1, 1)
Reason : If f ( a) = f (b ), then Rolles theorem is applicable for x ∈ (a, b)
g (–1) ≠ 0 and Rolles theorem is not applicable to \(f(x)=\frac{x^{2}-1}{g(x)}\) in [–1, 1], then g(x) has atleast one root
in (–1, 1)
Reason : If f ( a) = f (b ), then Rolles theorem is applicable for x ∈ (a, b)
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(C) If Assertion is true, Reason is false.
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