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  4. If f(x)=|x|3, then f'(0) is equal to

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Q. If $ f(x)=|x{{|}^{3}}, $ then $ f'(0) $ is equal to

Rajasthan PETRajasthan PET 2001

Solution:

$ f(x)=|x{{|}^{3}} $
$ f(x)=\left\{ \begin{matrix} {{x}^{3}}, & x>0 \\ 0, & x=0 \\ -{{x}^{3}}, & x<0 \\ \end{matrix} \right. $
$ \Rightarrow $ $ f'(x)=\left\{ \begin{matrix} 3{{x}^{3}}, & x>0 \\ 0, & x=0 \\ -3{{x}^{2}}, & x<0 \\ \end{matrix} \right. $