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  • If f (x) = | x | ^ 3, show that f ''(x) exists for all real x and find it.

 Q18  Iff (x) = |x|^3, show that f ''(x) exists for all real x and find it.

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best_answer

Given function is
f (x) = |x|^3
f(x)\left\{\begin{matrix} -x^3 & x<0\\ x^3 & x>0 \end{matrix}\right.
Now, differentiate in both the cases
f(x)= x^3\\ f^{'}(x)=3x^2\\ f^{''}(x)= 6x
And
f(x)= -x^3\\ f^{'}(x)=-3x^2\\ f^{''}(x)= -6x
In both, the cases f ''(x) exist
Hence, we can say that f ''(x) exists for all real x
and values are 
f^{''}(x)\left\{\begin{matrix} -6x &x<0 \\ 6x& x>0 \end{matrix}\right.
 

Posted by

Gautam harsolia

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