If \[f(x)=sgn ({{x}^{3}})\], then [DCE 2001] – McqOptions

MCQOPTIONS

1.	If \[f(x)=sgn ({{x}^{3}})\], then [DCE 2001]
A.	f is continuous but not derivable at \[x=0\]
B.	\[f'({{0}^{+}})=2\]
C.	\[f'({{0}^{-}})=1\]
D.	f is not derivable at \[x=0\]
Answer» E.

Discussion

No Comment Found

Related MCQs

The domain of the derivative of the function \[f(x)=\left\{ \begin{align} & {{\tan }^{-1}}x\ \ \ \ \ ,\ |x|\ \le 1 \\ & \frac{1}{2}(|x|\ -1)\ ,\ |x|\ >1 \\ \end{align} \right.\] is [IIT Screening 2002]
The function \[f(x)=\frac{{{\sec }^{-1}}x}{\sqrt{x-[x]}},\] where [.] denotes the greatest integer less than or equal to x is defined for all x belonging to
The function f satisfies the functional equation \[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\] for all real \[x\ne 1\]. The value of \[f(7)\] is [Kerala (Engg.) 2005]
If \[f(x)=\frac{x-|x|}{|x|}\], then \[f(-1)=\] [SCRA 1996]
If x is real, then value of the expression \[\frac{{{x}^{2}}+14x+9}{{{x}^{2}}+2x+3}\] lies between [UPSEAT 2002]
If \[f(x)=\left\{ \begin{align} & \,\,\,\,\,\,\,\,\,\,\,\,1,\,\,x<0 \\ & 1+\sin x,\,\,0\le x<\frac{\pi }{2} \\ \end{align} \right.\]then \[f'(0)=\] [MP PET 1994]
Suppose \[f(x)\] is differentiable at \[x=1\] and \[\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}f(1+h)=5\] , then \[f'(1)\] equals [AIEEE 2005]
The function \[f(x)={{x}^{2}}\,\,\sin \frac{1}{x},\,x\ne \,0,\,\,f(0)\,=0\] at \[x=0\] [MP PET 2003]
The domain of the function \[f(x)=\frac{1}{{{\log }_{10}}(1-x)}+\sqrt{x+2}\] is [DCE 2000]
If function \[f(x)=\frac{1}{2}-\tan \left( \frac{\pi x}{2} \right)\]; \[(-1<x<1)\] and \[g(x)=\sqrt{3+4x-4{{x}^{2}}}\], then the domain of gof is [IIT 1990]