If `f(x)=|x|^(3)`, then `f'`(0) equals

Options

A. 0
B. 43832
C. `-1`
D. `-1//2`

Answer

A

Explanation

`f(x)=|x|^(2)={{:(0,x=0),(x^(3),x gt 0),(-x^(3),x lt 0):}`
Now, `Tf'(0)=underset(h to 0)(lim)(h^(3)-0)/(-h)=0`
and `Lf'(0)=underset(hto0)(lim)(-h^(3)-0)/(-h)=0`
`becauseRf(0)=Lf'(0)=0`
`thereforef'(0)=0`