Question:
The function $f(x)=1+|\cos x|$ is
(a) continuous no where
(b) continuous everywhere
(c) not differentiable at $x=0$
(d) not differentiable at $x=n \pi, n \in Z$
Solution:
(b) continuous everywhere
Graph of the function $f(x)=1+|\cos x|$ is as shown below:
From the graph, we can see that $f(x)$ is everywhere continuous but not differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$