Let f:[a,b]\to[1,\infty) be a continuous function and let g:\mathbb{R}\to\mathbb{R} be defined as g(x)=\{\table0,\text{if},x < a \text{,};\int^{x}_{a}f(t)dt,\text{if}, a \leq x \leq b\text{, }; \int^{b}_af(t)dt,\text{if}, x > b Then [JEE Adv 2014 P1]

g(x) is continuous but not differentiable at a

g(x) is continuous but not differentiable at b

g(x) is continuous and differentiable at either a or b but not both

Limits, Continuity and Differentiability

Section: Mathematics

Question : 38 of 51

Marks: +1, -0

Let f:[a,b]→[1,∞) be a continuous function and let g:ℝ→ℝ be defined as
g(x)={

Then

[JEE Adv 2014 P1]

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