Question

Найдите промежутки монотонности функции !

Answer 1

$y= \frac{2x^2-3x+4}{x+2}\; ;\; \; \; x\ne -2\\\\y'= \frac{(4x-3)(x+2)-(2x^2-3x+4)}{(x+2)^2}= \frac{2(x+5)(x-1)}{(x+2)^2} =0\\\\x=-5\; ;\; \; x=1\; ;\; \; x\ne -2\\\\Znaki\; \; y':\; \; +++(-5)---(-2)---(1)+++\\\\.\qquad \qquad \qquad \nearrow(-5)\quad \searrow \quad (-2)\; \; \; \searrow \quad (1)\quad \nearrow \\\\y(x)\; vozrastaet\; \; (-\infty ,-5)\; ;\; (1,+\infty )\\\\y(x) \; ybuvaet\; \; (-5,-2)\; ;\; (-2,1)\\\\x_{max}=-5\\\\x_{min}=1$