Знайдіть найбільше і найменше значення функції: на відрізку (-3;0)
Простите пожалуйста, а что означают те минусы с плюсами(это пряма или я ошиблась)?
Это на числовой прямй расставлены знаки производной в каждом промежутке.
Спасибо!)
Я добавила к ответу пояснение.
![y= \frac{x^2+8}{x-1} \; ,\; \; x\in [-3,0\, ]\\\\y'= \frac{2x(x-1)-(x^2+8)\cdot 1}{(x-1)^2} = \frac{x^2-2x-8}{(x-1)^2} = \frac{(x+2)(x-4)}{(x-1)^2} =0\; ,\; x\ne 1](https://tex.z-dn.net/?f=y%3D+%5Cfrac%7Bx%5E2%2B8%7D%7Bx-1%7D+%5C%3B+%2C%5C%3B+%5C%3B+x%5Cin+%5B-3%2C0%5C%2C+%5D%5C%5C%5C%5Cy%27%3D+%5Cfrac%7B2x%28x-1%29-%28x%5E2%2B8%29%5Ccdot+1%7D%7B%28x-1%29%5E2%7D+%3D+%5Cfrac%7Bx%5E2-2x-8%7D%7B%28x-1%29%5E2%7D+%3D+%5Cfrac%7B%28x%2B2%29%28x-4%29%7D%7B%28x-1%29%5E2%7D+%3D0%5C%3B+%2C%5C%3B+x%5Cne+1 "y= \frac{x^2+8}{x-1} \; ,\; \; x\in [-3,0\, ]\\\\y'= \frac{2x(x-1)-(x^2+8)\cdot 1}{(x-1)^2} = \frac{x^2-2x-8}{(x-1)^2} = \frac{(x+2)(x-4)}{(x-1)^2} =0\; ,\; x\ne 1")
![+++[-2\, ]---(1)---[\, 4\, ]+++](https://tex.z-dn.net/?f=%2B%2B%2B%5B-2%5C%2C+%5D---%281%29---%5B%5C%2C+4%5C%2C+%5D%2B%2B%2B "+++[-2\, ]---(1)---[\, 4\, ]+++")
![x_{max}=-2\in [-3,0\, ]\; \; ;\; \; \; x_{min}=4\notin [-3,0\, ]\\\\y(-2)= \frac{4+8}{-3} =-4\\\\y(-3)= \frac{9+8}{-4} =-\frac{17}{4}=-4\frac{1}{4}\\\\y(0)=-8\\\\y_{naimenshee}=-8\\\\y_{naibolshee}=-4](https://tex.z-dn.net/?f=x_%7Bmax%7D%3D-2%5Cin+%5B-3%2C0%5C%2C+%5D%5C%3B+%5C%3B+%3B%5C%3B+%5C%3B+%5C%3B+x_%7Bmin%7D%3D4%5Cnotin+%5B-3%2C0%5C%2C+%5D%5C%5C%5C%5Cy%28-2%29%3D+%5Cfrac%7B4%2B8%7D%7B-3%7D+%3D-4%5C%5C%5C%5Cy%28-3%29%3D+%5Cfrac%7B9%2B8%7D%7B-4%7D+%3D-%5Cfrac%7B17%7D%7B4%7D%3D-4%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5Cy%280%29%3D-8%5C%5C%5C%5Cy_%7Bnaimenshee%7D%3D-8%5C%5C%5C%5Cy_%7Bnaibolshee%7D%3D-4 "x_{max}=-2\in [-3,0\, ]\; \; ;\; \; \; x_{min}=4\notin [-3,0\, ]\\\\y(-2)= \frac{4+8}{-3} =-4\\\\y(-3)= \frac{9+8}{-4} =-\frac{17}{4}=-4\frac{1}{4}\\\\y(0)=-8\\\\y_{naimenshee}=-8\\\\y_{naibolshee}=-4")