Differentiation Question 295

Question: The derivative of $ f(x)=|x{{|}^{3}} $ at $ x=0 $ is

[RPET 2001; Kurukshetra CEE 2002]

Options:

A) 0

B) 1

C) -1

D) Not defined

Show Answer

Answer:

Correct Answer: A

Solution:

$ f(x)=|x{{|}^{3}} $

Therefore $ {f}’(x)=3|x{{|}^{2}}\frac{d}{dx}|x| $

At $ x=0 $ , $ {f}’(x)=0.\frac{d}{dx}|x| $ , $ {f}’(x)=0 $ .