The set of points where the function f(x)=x∣x∣ is differentiable is?

The set of points where the function f(x)=x∣x∣ is differentiable is?

Answer is (−∞,∞)

Consider the given function.
f(x)=x∣x∣

f(x)= 
⎩
⎪
⎪
⎨
⎪
⎪
⎧
​
  
x 
2
 ,
−x 
2
 ,
0
​
  
x>0
x<0
x=0
​
 

Since, it is polynomial function.
Hence, it is differentiable at (−∞,∞).

Last Updated on October 10, 2021 by OrderTrackings Team

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