- Home
- Standard 11
- Mathematics
જો ${\rm{x}}$ વાસ્તવિક હોય , તો $\,\frac{{3{x^2} + \,9x\, + \,17}}{{3{x^2}\, + \,9x\, + \,7}}$ નું મહતમ મૂલ્ય કેટલું થાય ?
$1$
$17/7$
$1/4$
$41$
Solution
$\,y\,\, = \,\,\frac{{3{x^2}\, + \,\,9x\,\, + \,\,7\,\, + \,\,10}}{{3{x^2}\, + \,\,9x\,\, + \,\,7}}$
$y\,\, = \,\,1\,\, + \,\,\frac{{10}}{{3{x^2}\, + \,\,9x\,\, + \,\,7}}$
$y\,\, = \,\,1\,\, + \,\,\frac{{10}}{p}$
$p\,$ ન્યૂનતમ હોય , તો $y$ મહતમ થાય
${\rm{p}}\,\, = \,\,{\rm{3}}{{\rm{x}}^{\rm{2}}}{\rm{ }} + \,\,{\rm{9x}}\,\, + \,\,{\rm{7}}$
${{\rm{p}}_{{\rm{min}}}}\, = \,\,\frac{{{\rm{ – D}}}}{{{\rm{4a}}}}\,\, = \,\,\frac{{{\rm{ – (81}}\,\,{\rm{ – }}\,\,{\rm{12}}\,\, \times \,\,{\rm{7)}}}}{{{\rm{12}}}}\,\,\,\,$
$ \Rightarrow \,\,{{\rm{p}}_{{\rm{min}}}}{\rm{ }} = \,\,\frac{{\rm{1}}}{{\rm{4}}}$
${{\rm{y}}_{{\rm{max}}}}\, = \,\,{\rm{1}}\,\, + \,\,\frac{{{\rm{10}}}}{{{\rm{1/4}}}}\,\, = \,\,{\rm{41 }}$
