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Limits Continuity and Differentiability question

2014 · Shift 1 · Q32
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  2. /JEE Advanced
  3. /Mathematics
  4. /Limits Continuity and Differentiability
  5. /2014 · Shift 1 · Q32

Limits Continuity and Differentiability question

2014 · Shift 1 · Q32

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+3 / −1
Let f:(a,b)→[1,∞)f:(a,b) \to [1,\infty )f:(a,b)→[1,∞) be a continuous function and g : R →\to→ R be defined as g(x)={0,xbg(x) = \left\{ {\begin{matrix} 0 & , & {x b} \\ \end{matrix} } \right.g(x)={0​,​xb​ Then,
  1. A
    g(x) is continuous but not differentiable at a
  2. B
    g(x) is differentiable on R
  3. C
    g(x) is continuous but not differentiable at b
  4. D
    g(x) is continuous and differentiable at either a or b but not both
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