Let be a function defined by f(x)= cases t:0 t x ,&0 x , 2+ x,&x>

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f:[0,\infty)\rightarrow[0,3]

be a function defined by

f(x)=\begin{cases}\max\{\sin t:0\leq t\leq x\},&0\leq x\leq\pi,\\2+\cos x,&x>\pi.\end{cases}

Then which of the following is true? (a)

f

is continuous everywhere but not differentiable exactly at one point in

(0,\infty)

. (b)

f

is differentiable everywhere in

(0,\infty)

. (c)

f

is not continuous exactly at two points in

(0,\infty)

. (d)

f

is continuous everywhere but not differentiable exactly at two points in

(0,\infty)