Let f : [ a , b ] → [1, ∞) be a continuous function and let g : R → R be defined as g(x)=…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : [a, b] → [1, ∞) be a continuous function and let
g : R → R be defined as \[g(x)=\left\{\begin{array}{llc} 0 & \text { if } & xb \end{array}\right.\]
Then
g : R → R be defined as \[g(x)=\left\{\begin{array}{llc} 0 & \text { if } & xb \end{array}\right.\]
Then
- g(x) is continuous but not differentiable at a
- g(x) is differentiable on R
- g(x) is continuous but not differentiable at b
- g(x) is continuous and differentiable at either a or b but not both
Answer
(B) g ( x ) is differentiable on R
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