![L(x)=f(a)+f'(a)(x-a)](https://tex.z-dn.net/?f=L%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29)
- уравнение касательной к функции
![f(x)](https://tex.z-dn.net/?f=f%28x%29)
в точке
![x=a](https://tex.z-dn.net/?f=x%3Da)
1)
![f'(x)=[x^6+4x^3-1]'=6x^5+12x^2\\\\ f'(-1)=-6+12=6\\\\ f(-1)=1-4-1=-4\\\\ L(x)=-4+6*(x-(-1))=-4+6(x+1) =-4+6x+6=\\\\=L(x)=6x+2](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Bx%5E6%2B4x%5E3-1%5D%27%3D6x%5E5%2B12x%5E2%5C%5C%5C%5C+f%27%28-1%29%3D-6%2B12%3D6%5C%5C%5C%5C+f%28-1%29%3D1-4-1%3D-4%5C%5C%5C%5C+L%28x%29%3D-4%2B6%2A%28x-%28-1%29%29%3D-4%2B6%28x%2B1%29+%3D-4%2B6x%2B6%3D%5C%5C%5C%5C%3DL%28x%29%3D6x%2B2)
3)
![f(x)=\sqrt{5-4x}\\\\ f'(x)=\frac{(5-4x)'}{2\sqrt{5-4x}}=\frac{-4}{2\sqrt{5-4x}}=-\frac{2}{\sqrt{5-4x}}\\\\ f(1)=\sqrt{5-4}=1\\\\ f'(1)=-\frac{2}{1}=-2\\\\ L(x)=1+(-2)*(x-1)=1-2x+2=-2x+3\\\\ tg(\alpha)=-2\ \textless \ 0](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7B5-4x%7D%5C%5C%5C%5C+f%27%28x%29%3D%5Cfrac%7B%285-4x%29%27%7D%7B2%5Csqrt%7B5-4x%7D%7D%3D%5Cfrac%7B-4%7D%7B2%5Csqrt%7B5-4x%7D%7D%3D-%5Cfrac%7B2%7D%7B%5Csqrt%7B5-4x%7D%7D%5C%5C%5C%5C+f%281%29%3D%5Csqrt%7B5-4%7D%3D1%5C%5C%5C%5C+f%27%281%29%3D-%5Cfrac%7B2%7D%7B1%7D%3D-2%5C%5C%5C%5C+L%28x%29%3D1%2B%28-2%29%2A%28x-1%29%3D1-2x%2B2%3D-2x%2B3%5C%5C%5C%5C+tg%28%5Calpha%29%3D-2%5C+%5Ctextless+%5C+0)
2) - скриншотами своего же решения ранее
тупой угол
Решение представлено на фотографии
(25а-4ав)2=а(5-2в)(5+2в)
3а в квадрате -6а+3=3а в квадрате -3а-3а+3= 3а(а-1)-3(а-1)=(3а-3)(а-1)
(3x-1)(3x+1)+(3x+1)в квад=9х в квад -1+9х в квад +6х +1= 18х в квад+6х=6х(3х+1)