If f : [–1, 1] → R is a continuously differentiable function such that f (1) > f (–1) and…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
If f : [–1, 1] → R is a continuously differentiable function such that f (1) > f (–1) and | f ′(y)| < 1 for all y ∈ [–1, 1] then
- there exists an x ∈ [–1, 1] such that f ′(x) > 0
- there exists an x ∈ [–1, 1] such that f ′(x) < 0
- f (1) < f (–1) + 2
- f (–1) . f (1) < 0
Answer
(A) there exists an x ∈ [–1, 1] such that f ′ (x) > 0, (C) f (1) f (–1) + 2
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