6. Application of derivatives — ગણિત ધોરણ 12 સાયન્સ — Question

$ \Rightarrow \,{\text{z}}\,\, = \,\,{\text{logy}}\,\, = \,\,{\text{plogsinx}}\,\, + \,\,{\text{qlogcosx}}\,\, $

$\Rightarrow \,\,\frac{{{\text{dz}}}}{{{\text{dx}}}}\,\, = \,\,p\cot x\,\, - \,\,q\tan x,$

$\frac{{{d^2}z}}{{d{x^2}}}\,\, = \, - p\cos e{c^2}x\, - \,\,q{\sec ^2}x$

હવે $\,\frac{{{\text{dz}}}}{{{\text{dx}}}}\,\, = \,\,0\,\, \Rightarrow {\tan ^2}x\,\, = \,\,p/q\,\,\, \Rightarrow \,\tan x\,\, = \,\,\sqrt {p\,/q} $

ઉપરાંત પછી $\frac{{{{\text{d}}^{\text{2}}}z}}{{d{x^2}}}$ ચોકકસ ઋણ છે. 

તેથી, ${\text{x}}\, = \,{\tan ^{ - 1}}\,\sqrt {{\text{p/q}}} $ એ ${\text{z}}$ ના મહતમ બિંદુ છે. દા.ત. તે $\,\,{\text{y}}$ છે.