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

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f:[0,∞)→[0,3]f:[0,\infty)\to[0,3] be defined by f(x)={max⁡{sin⁡t:0≤t≤x},0≤x≤π,2+cos⁡x,x>π.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) ff is continuous everywhere but not differentiable exactly at one point in (0,∞)(0,\infty). (b) ff is differentiable everywhere in (0,∞)(0,\infty). (c) ff is not continuous exactly at two points in (0,∞)(0,\infty). (d) ff is continuous everywhere but not differentiable exactly at two points in (0,∞)(0,\infty).

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