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the set of all the points where the function f(x)=x|x| is twice differentiable is

the set of all the points where the function f(x)=x|x| 
is twice differentiable is

Grade:11

1 Answers

Arun
25757 Points
6 years ago
f(x) = x|x| = x²,  x>0
               = -x²,   x
 
f'(x) = 2x,  x>0
        = -2x,  x
 
f''(x) = 2,    x>0
        = -2,    x
f''(x) exists at every point except x=0
 
Thus f(x) is twice differentiable on R - {0}

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