SOLUTION: Consider the function f(x) = 1/2 (x + |x| ). Discuss continuity and smoothness for this function. Where is it discontinuous? Where is it not smooth? Also find each of the following

Question 1020689: Consider the function f(x) = 1/2 (x + |x| ). Discuss continuity and smoothness for this function. Where is it discontinuous? Where is it not smooth? Also find each of the following quantities: f(3), f(-4), f'(3), f'(-4).
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!

it is not discontinuous
It is not smooth where x=0. There is a corner.
f(3)=(1/2)(3+abs(3))=3
f(-4)=(1/2)(-4+abs(-4))=0
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