MCQ
$\frac{{{\text{1}}\,{\text{ - }}\,{\text{x}}\, + \,{{\text{x}}^{\text{2}}}}}{{1\, + \,x\, + \,{x^2}}}$ ન્યૂનતમ મૂલ્ય ક્યૂ છે. $?$
- A$0$
- B$1/3$
- C$1$
- D$3$
$\, = \,\,{\text{1}}\,\,{\text{ - }}\,\frac{{{\text{2x}}}}{{{\text{1}}\, + \,{\text{x}}\, + \,{{\text{x}}^{\text{2}}}}}\,\, $
$= \,\,1\,\, - \,\,\frac{2}{{\,\frac{1}{x}\, + \,1\, + \,x}}\,\, $
$= \,\,1\,\, - \,\frac{2}{z}$
$y\,$ ન્યૂનતમ છે. જ્યારે $\frac{{\text{2}}}{{\text{z}}}$ મહતમ છે. અથવા જ્યારે $\,\frac{{{\text{dz}}}}{{{\text{dx}}}}\,\, = \,\,0\,\, \Rightarrow \,x\,\, = \,\, \pm \,1$
જ્યારે ${\text{x}}\, = \,{\text{1,}}\,\,\frac{{{{\text{d}}^{\text{2}}}z}}{{d{x^2}}}\,\, = \,\,2\,\, > \,0$
$\therefore \,\,{\text{x}}\, = \,{\text{1}}\,$ આગળ $\,{\text{z}} $ ન્યૂનતમ છે, પરિણામે ${\text{y}}$ ન્યૂનતમ છે.
$\therefore \,{{\text{(y)}}_{{\text{min}}}}\, = \,\,1\, - \,\,\frac{2}{3}\,\, = \,\,\frac{1}{3}$
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