Consider the functions defined implicitly by the equation y 3 – 3 y + x = 0 on various…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Consider the functions defined implicitly by the equation y3 – 3y + x = 0 on various intervals in the real line.
If x ∈ (– ∞, – 2) ∪ (2, ∞), the equation implicitly defines a unique real valued differentiable function y = f (x).
If x ∈ (–2, 2), the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0 .
If x ∈ (– ∞, – 2) ∪ (2, ∞), the equation implicitly defines a unique real valued differentiable function y = f (x).
If x ∈ (–2, 2), the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0 .
- 2g(–1)
- 0
- –2g(1)
- 2g(1)
Answer
(D) 2 g (1)
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