Найдите критические точки функции f(x). Если есть экстремум, то определите среди них максимум и минимум: Не получается упростить, получаю
ошибка в производной
у меня
Спасибо большое!!!
![f(x)= \frac{x^3-1}{x^4} \; ,\; \; \; \; ODZ:\; \; x\ne 0\\\\f'(x)= \frac{3x^2\cdot x^4-(x^3-1)\cdot 4x^3}{x^8} = \frac{x^3(3x^3-4x^3+4)}{x^8} = \frac{4-x^3}{x^5} =0\\\\4-x^3=0\; ,\; x\ne 0\\\\x=\sqrt[3]{4}\approx 1,59\; ;\; x=0 \; \; -\; kriticheskie \; tochki\\\\Znaki\; f'(x):\; \; \; ---(0)+++(\sqrt[3]4)---](https://tex.z-dn.net/?f=f%28x%29%3D+%5Cfrac%7Bx%5E3-1%7D%7Bx%5E4%7D+%5C%3B+%2C%5C%3B+%5C%3B+%5C%3B+%5C%3B+ODZ%3A%5C%3B+%5C%3B+x%5Cne+0%5C%5C%5C%5Cf%27%28x%29%3D+%5Cfrac%7B3x%5E2%5Ccdot+x%5E4-%28x%5E3-1%29%5Ccdot+4x%5E3%7D%7Bx%5E8%7D+%3D+%5Cfrac%7Bx%5E3%283x%5E3-4x%5E3%2B4%29%7D%7Bx%5E8%7D+%3D+%5Cfrac%7B4-x%5E3%7D%7Bx%5E5%7D+%3D0%5C%5C%5C%5C4-x%5E3%3D0%5C%3B+%2C%5C%3B+x%5Cne+0%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B4%7D%5Capprox+1%2C59%5C%3B+%3B%5C%3B+x%3D0+%5C%3B+%5C%3B+-%5C%3B+kriticheskie+%5C%3B+tochki%5C%5C%5C%5CZnaki%5C%3B+f%27%28x%29%3A%5C%3B+%5C%3B+%5C%3B+---%280%29%2B%2B%2B%28%5Csqrt%5B3%5D4%29--- "f(x)= \frac{x^3-1}{x^4} \; ,\; \; \; \; ODZ:\; \; x\ne 0\\\\f'(x)= \frac{3x^2\cdot x^4-(x^3-1)\cdot 4x^3}{x^8} = \frac{x^3(3x^3-4x^3+4)}{x^8} = \frac{4-x^3}{x^5} =0\\\\4-x^3=0\; ,\; x\ne 0\\\\x=\sqrt[3]{4}\approx 1,59\; ;\; x=0 \; \; -\; kriticheskie \; tochki\\\\Znaki\; f'(x):\; \; \; ---(0)+++(\sqrt[3]4)---")
![x=\sqrt[3]4](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D4 "x=\sqrt[3]4")
![y(\sqrt[3]4)=\frac{3}{4\sqrt[3]4}](https://tex.z-dn.net/?f=y%28%5Csqrt%5B3%5D4%29%3D%5Cfrac%7B3%7D%7B4%5Csqrt%5B3%5D4%7D "y(\sqrt[3]4)=\frac{3}{4\sqrt[3]4}")