JEE Main 202127 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002Let f:[0,∞)→[0,3]f:[0,\infty ) \to [0,3]f:[0,∞)→[0,3] be a function defined by f(x)={max{sint:0≤t≤x},0≤x≤π2+cosx,x>πf(x) = \left\{ {\matrix{ {\max \{ \sin t:0 \le t \le x\} ,} & {0 \le x \le \pi } \cr {2 + \cos x,} & {x > \pi } \cr } } \right.f(x)={max{sint:0≤t≤x},2+cosx,0≤x≤πx>π Then which of the following is true?AOption A. f is continuous everywhere but not differentiable exactly at one point in (0, ∞\infty∞)BOption B. f is differentiable everywhere in (0, ∞\infty∞)COption C. f is not continuous exactly at two points in (0, ∞\infty∞)DOption D. f is continuous everywhere but not differentiable exactly at two points in (0, ∞\infty∞)CheckSkip · show solution
