Подставляем 3= 3х+3
3х= 3-3
3х =0
Х= 0:3
Х=0
Выражение записанное под корнем чётной степени должно быть неотрицательным то есть ≥ 0 .
![1)\sqrt{3-x}\\\\3-x\geq0\\\\-x\geq-3\\\\x\leq3\\\\Otvet:\boxed{x\in(-\infty;3]}](https://tex.z-dn.net/?f=1%29%5Csqrt%7B3-x%7D%5C%5C%5C%5C3-x%5Cgeq0%5C%5C%5C%5C-x%5Cgeq-3%5C%5C%5C%5Cx%5Cleq3%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%28-%5Cinfty%3B3%5D%7D)
![2)\sqrt{3-3x}\\\\3-3x\geq0\\\\-3x\geq-3\\\\x\leq 1\\\\Otvet:\boxed{x\in(-\infty;1]}](https://tex.z-dn.net/?f=2%29%5Csqrt%7B3-3x%7D%5C%5C%5C%5C3-3x%5Cgeq0%5C%5C%5C%5C-3x%5Cgeq-3%5C%5C%5C%5Cx%5Cleq%201%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%28-%5Cinfty%3B1%5D%7D)
![3)\sqrt{-4x}\\\\-4x\geq0\\\\x\leq 0\\\\Otvet:\boxed{x\in(-\infty;0]}](https://tex.z-dn.net/?f=3%29%5Csqrt%7B-4x%7D%5C%5C%5C%5C-4x%5Cgeq0%5C%5C%5C%5Cx%5Cleq%200%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%28-%5Cinfty%3B0%5D%7D)
![4)\sqrt{x-3,5}\\\\x-3,5\geq0\\\\x\geq3,5\\\\Otvet:\boxed{x\in[3,5;+\infty)}](https://tex.z-dn.net/?f=4%29%5Csqrt%7Bx-3%2C5%7D%5C%5C%5C%5Cx-3%2C5%5Cgeq0%5C%5C%5C%5Cx%5Cgeq3%2C5%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%5B3%2C5%3B%2B%5Cinfty%29%7D)
![5)\sqrt{3x+12}\\\\3x+12\geq0\\\\3x\geq -12\\\\x\geq-4\\\\Otvet:\boxed{x\in[-4;+\infty)}](https://tex.z-dn.net/?f=5%29%5Csqrt%7B3x%2B12%7D%5C%5C%5C%5C3x%2B12%5Cgeq0%5C%5C%5C%5C3x%5Cgeq%20-12%5C%5C%5C%5Cx%5Cgeq-4%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%5B-4%3B%2B%5Cinfty%29%7D)
![6)\sqrt{7-0,2x}\\\\7-0,2x\geq0 \\\\-0,2x\geq -7\\\\x\leq35\\\\Otvet:\boxed{x\in(-\infty;35]}](https://tex.z-dn.net/?f=6%29%5Csqrt%7B7-0%2C2x%7D%5C%5C%5C%5C7-0%2C2x%5Cgeq0%20%5C%5C%5C%5C-0%2C2x%5Cgeq%20-7%5C%5C%5C%5Cx%5Cleq35%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%28-%5Cinfty%3B35%5D%7D)
<span>а2-6а-16 = </span>а2-8а+2а-16 = а(а-8)+2(а-8)=(а-8)(а+2)
По физическому смыслу производной: скорость – есть производная от пути по времени.
![\sf v(t)=x'(t)=(3t^2-12t+8)'=6t-12\\v(t)=0;\\ 6t-12=0\\ t=2~~c](https://tex.z-dn.net/?f=%5Csf+v%28t%29%3Dx%27%28t%29%3D%283t%5E2-12t%2B8%29%27%3D6t-12%5C%5Cv%28t%29%3D0%3B%5C%5C+6t-12%3D0%5C%5C+t%3D2~~c)
В момент времени t = 2 c скорость равна нулю.