Calcus

Question

1. f(x)=|x|+ |x+1|+ |x+2| is diffrentiable at x= 1 How it 1 Please Explain ?

Answer 1

Function is continuous at x = 1

=> diffrentiable @ x = 1

Comments

if function is continous then it need not be differentiable..eg. f(x) =│x│ is continuous but not differentiable at 0
since f'(x) is -1,0and1 respectively at 0-,0 and 0+

continuity≠>differentiable
and differentiable=>continuity