• # question_answer Let f be a function defined by - $f(x)=\left\{ \begin{matrix} \frac{\tan x}{x} & ,x\ne 0 \\ 1 & ,x=0 \\ \end{matrix} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ne 0$ Statement -1 : x = 0 is point of minima of f Statement-2 : f'(0) =0.     AIEEE  Solved  Paper (Held On 11 May  2011) A)  Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1. B)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1 C)  Statement-1 is true, Statement-2 is false. D)  Statement-1 is false, Statement-2 is true.

$f(x)=\left\{ \begin{matrix} \frac{\tan x}{x} & x\ne 0 \\ 1 & x=0 \\ \end{matrix} \right.$ In right neighborhood of '0'                                     tan x > x $\frac{\tan x}{x}>1$ In left neighborhood of '0'                                              tan x < x $\frac{\tan x}{x}>1$                     as (x < 0) at x = 0,                                f (x) = 1 $\Rightarrow$ x = 0 is point of minima so statement 1 is true. statement 2 obvious