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Limits Continuity and Differentiability question

2011 · Shift 1 · Q41
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  2. /JEE Advanced
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  4. /Limits Continuity and Differentiability
  5. /2011 · Shift 1 · Q41

Limits Continuity and Differentiability question

2011 · Shift 1 · Q41

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1
Let f : R →\to→ R be a function such that f(x+y)=f(x)+f(y), ∀x,y∈Rf(x + y) = f(x) + f(y),\,\forall x,y \in Rf(x+y)=f(x)+f(y),∀x,y∈R. If f(x) is differentiable at x = 0, then
  1. A
    f(x) is differentiable only in a finite interval containing zero.
  2. B
    f(x) is continuous ∀x∈R\forall x \in R∀x∈R.
  3. C
    f'(x) is constant ∀x∈R\forall x \in R∀x∈R.
  4. D
    f(x) is differentiable except at finitely many points.
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