While plotting the function mentioned below using a graphing software quickly gives the answer, I am unable to understand how one must solve it. I have studied some properties of modulus functions and would have been able to draw the graph if the $e^x$ was missing.
Find where the function defined on the real line given by $f(x) = |x| + |x+1| + e^x$ is not differentiable.
Could you please let me know how this question must be approached. Moreover, a hint regarding how a question such as the one mentioned above can be solved if $e^x$ was replaced by some other function like $\log(x)$ or $\sin(x)$