Let f(x) = l ( 3 - , ( 1/x ) ) , | x |, , , , ,x 0 0, , , , , , ,… - Vidyadip

MCQ

Let $f(x) = \left\{ \begin{array}{l} \left( {3 - \sin \,\left( {1/x} \right)} \right)\,\left| x \right|,\,\,\,\,x \ne 0\\ 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0\,\, \end{array} \right.\,$ . Then at $x = 0 , f$ has a

A
maxima
B
minima
C
Neither maxima nor minima
D
Point of discontinuity

✓

Answer

$f$ is continous at $\mathrm{x}=0$
Further $f(0+h) > f(0)$ and $f(0-h) > f(0),$
for positive $'h\ '.$
Hence $f$ has minimum value at $x=0$.

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