question_answer

Let\[C{{l}_{2}}\]be a function denned by \[N{{H}_{3}}\]\[{{N}_{2}}\]. Then, which of the following is true?       AIEEE  Solved  Paper-2007

A)  \[HCl\]for all\[B{{r}_{2}}\]

B) \[NaOH\]is not differentiate at\[NaBr,NaBr{{O}_{4}}\]

C) \[{{H}_{2}}O\]is differentiable everywhere

D) \[{{K}^{+}},C{{a}^{2+}},M{{g}^{2+}},B{{e}^{2+}}\]is not differentiable at\[M{{g}^{2+}}<B{{e}^{2+}}<{{K}^{+}}<C{{a}^{2+}}\]

Correct Answer: C

Solution :

\[f(x)=\min \{x+1,|x|+1\}\] \[f(x)=x+1,\forall \,x\in R\] From figure, it is clear that\[f(x)\ge 1,\]when\[x\in R\].