Question

Найдите y наим.

y=11+ (11sqrt3 pi)/12-(11-sqrt3)/2 *x-11sqrt3 cosx (0 до pi/2)

Answer 1

Ответ:

$y'=(11+\frac{11\sqrt{3}\pi }{12} -\frac{11\sqrt{3} }{2}x-11\sqrt{3} \cos x )'=-\frac{11\sqrt{3} }{2} -(11\sqrt{3}\cdot (-\sin x))=\frac{11\sqrt{3}}{2} \cdot (2 \sin x-1)\\\\y'=0 => \frac{11\sqrt{3}}{2} \cdot (2 \sin x-1)=0\\\\2 \sin x=1 => \sin x = \frac{1}{2} \\\\x = \frac{\pi}{6} + 2\pi n, n \in Z; x=\frac{5\pi}{6} +2\pi n, n \in Z$

$0<x<  \frac{\pi}{2} \\x = \frac{\pi}{6} \\\\y=11+\frac{11\sqrt{3}\pi }{12} -\frac{11\sqrt{3} }{2}\cdot  \frac{\pi}{6} -11\sqrt{3} \cos  (\frac{\pi}{6}) =11+\frac{11\sqrt{3}\pi }{12} -\frac{11\sqrt{3}\pi }{12} -11\sqrt{3} \cdot \frac{\sqrt{3}}{2} =11- \frac{11\cdot 3}{2} =\frac{22-33}{2} =-\frac{11}{2}$

Объяснение: