Functions Question 585
Question: If $ f(x)= \begin{cases} & ax^{2}+b;x\le 0 \\ & ,x^{2};x>0, \\ \end{cases} . $ possesses derivative at $ x=0 $ , then
Options:
A) $ a=0,b=0 $
B) $ a>0,=0 $
C) $ a\in R,=0 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x) $ possesses derivative at $ x=0 $ , so it is both continuous and differentiable at $ x=0 $ . Now $ f(0+0)=0 $ , $ f(0-0)=b,f(0)=b $ ,
$ \therefore b=0 $ Also $ Rf’(0)=0,Lf’(0)=0,\forall a\in R $ \ $ f’(0)=0 $ if $ b=0 $ .
BETA
