1.
![(x-1)(x+2)(x-4) ^{2} \leq 0, \\
(x-1)(x+2)(x-4) ^{2} = 0, \\
x_1=-2, x_2=1, x_3=4, \\
(x-4) ^{2} \geq 0, (x-1)(x+2) \leq 0, \\
-2 \leq x \leq 1, \\
x\in[-2;1]\cup\{4\}; \\
-2+(-1)+0+1+4=2.](https://tex.z-dn.net/?f=%28x-1%29%28x%2B2%29%28x-4%29+%5E%7B2%7D+%5Cleq+0%2C+%5C%5C+%0A%28x-1%29%28x%2B2%29%28x-4%29+%5E%7B2%7D+%3D+0%2C+%5C%5C+%0Ax_1%3D-2%2C+x_2%3D1%2C+x_3%3D4%2C+%5C%5C%0A%28x-4%29+%5E%7B2%7D+%5Cgeq+0%2C+%28x-1%29%28x%2B2%29+%5Cleq+0%2C+%5C%5C+%0A-2+%5Cleq+x+%5Cleq+1%2C+%5C%5C%0Ax%5Cin%5B-2%3B1%5D%5Ccup%5C%7B4%5C%7D%3B+%5C%5C%0A-2%2B%28-1%29%2B0%2B1%2B4%3D2. "(x-1)(x+2)(x-4) ^{2} \leq 0, \\
(x-1)(x+2)(x-4) ^{2} = 0, \\
x_1=-2, x_2=1, x_3=4, \\
(x-4) ^{2} \geq 0, (x-1)(x+2) \leq 0, \\
-2 \leq x \leq 1, \\
x\in[-2;1]\cup\{4\}; \\
-2+(-1)+0+1+4=2.")
2.
3.
0, \\
\left \left[ {{x=0,} \atop {x=2;}} \right. " alt="y=2,7e ^{3 x^{2} - x^{3}-4 } , x\in[1;3], \\
y'=2,7e ^{3 x^{2} - x^{3}-4 }\cdot(6x-3x^2), \\
y'=0, \ 8,1e ^{3 x^{2} - x^{3}-4 }\cdot x(2-x)=0, \\
e ^{3 x^{2} - x^{3}-4 }>0, \\
\left \left[ {{x=0,} \atop {x=2;}} \right. " align="absmiddle" class="latex-formula">
![x=1, y=2,7e ^{3\cdot1^{2}-1^{3}-4}=2,7e^{-2}, \\
x=2, y=2,7e ^{3\cdot2^{2}-2^{3}-4}=2,7 \\
x=3, y=2,7e ^{3\cdot3^{2}-3^{3}-4}=2,7e^{-4}, \\
\max\limits_{x\in[1;3]}y=2,7;\min\limits_{x\in[1;3]}y=2,7e^{-4}.](https://tex.z-dn.net/?f=x%3D1%2C+y%3D2%2C7e+%5E%7B3%5Ccdot1%5E%7B2%7D-1%5E%7B3%7D-4%7D%3D2%2C7e%5E%7B-2%7D%2C+%5C%5C%0Ax%3D2%2C+y%3D2%2C7e+%5E%7B3%5Ccdot2%5E%7B2%7D-2%5E%7B3%7D-4%7D%3D2%2C7+%5C%5C%0Ax%3D3%2C+y%3D2%2C7e+%5E%7B3%5Ccdot3%5E%7B2%7D-3%5E%7B3%7D-4%7D%3D2%2C7e%5E%7B-4%7D%2C+%5C%5C%0A%5Cmax%5Climits_%7Bx%5Cin%5B1%3B3%5D%7Dy%3D2%2C7%3B%5Cmin%5Climits_%7Bx%5Cin%5B1%3B3%5D%7Dy%3D2%2C7e%5E%7B-4%7D. "x=1, y=2,7e ^{3\cdot1^{2}-1^{3}-4}=2,7e^{-2}, \\
x=2, y=2,7e ^{3\cdot2^{2}-2^{3}-4}=2,7 \\
x=3, y=2,7e ^{3\cdot3^{2}-3^{3}-4}=2,7e^{-4}, \\
\max\limits_{x\in[1;3]}y=2,7;\min\limits_{x\in[1;3]}y=2,7e^{-4}.")
4.
![(3,4 \sqrt[3]{25 \sqrt{5} }+1,6 \sqrt{5 \sqrt[3]{25} }) ^{ -\frac{6}{11} } = (3,4 \sqrt[3]{5^2 \sqrt{5} }+1,6 \sqrt{5 \sqrt[3]{5^2} }) ^{ -\frac{6}{11} } = \\ = (3,4 \sqrt[3]{ \sqrt{5^4\cdot5} }+1,6 \sqrt{ \sqrt[3]{5^3\cdot5^2} }) ^{ -\frac{6}{11} } =(3,4 \sqrt[6]{ 5^5}+1,6 \sqrt[6]{5^5 }) ^{ -\frac{6}{11} } = \\ = (5\sqrt[6]{5^5 }) ^{ -\frac{6}{11} } = (5\cdot5^{ \frac{5}{6} }) ^{ -\frac{6}{11} } = (5^{ \frac{11}{6} }) ^{ -\frac{6}{11} } =5^{-1}= \frac{1}{5}= 0,2.](https://tex.z-dn.net/?f=%283%2C4+%5Csqrt%5B3%5D%7B25+%5Csqrt%7B5%7D+%7D%2B1%2C6+%5Csqrt%7B5+%5Csqrt%5B3%5D%7B25%7D+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D+%283%2C4+%5Csqrt%5B3%5D%7B5%5E2+%5Csqrt%7B5%7D+%7D%2B1%2C6+%5Csqrt%7B5+%5Csqrt%5B3%5D%7B5%5E2%7D+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D+%5C%5C+%3D+%283%2C4+%5Csqrt%5B3%5D%7B+%5Csqrt%7B5%5E4%5Ccdot5%7D+%7D%2B1%2C6+%5Csqrt%7B+%5Csqrt%5B3%5D%7B5%5E3%5Ccdot5%5E2%7D+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D%283%2C4+%5Csqrt%5B6%5D%7B+5%5E5%7D%2B1%2C6+%5Csqrt%5B6%5D%7B5%5E5+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D+%5C%5C+%3D++%285%5Csqrt%5B6%5D%7B5%5E5+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D+%285%5Ccdot5%5E%7B+%5Cfrac%7B5%7D%7B6%7D+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D+%285%5E%7B+%5Cfrac%7B11%7D%7B6%7D+%7D%29+%5E%7B+-%5Cfrac%7B6%7D%7B11%7D+%7D+%3D5%5E%7B-1%7D%3D+%5Cfrac%7B1%7D%7B5%7D%3D+0%2C2. "(3,4 \sqrt[3]{25 \sqrt{5} }+1,6 \sqrt{5 \sqrt[3]{25} }) ^{ -\frac{6}{11} } = (3,4 \sqrt[3]{5^2 \sqrt{5} }+1,6 \sqrt{5 \sqrt[3]{5^2} }) ^{ -\frac{6}{11} } = \\ = (3,4 \sqrt[3]{ \sqrt{5^4\cdot5} }+1,6 \sqrt{ \sqrt[3]{5^3\cdot5^2} }) ^{ -\frac{6}{11} } =(3,4 \sqrt[6]{ 5^5}+1,6 \sqrt[6]{5^5 }) ^{ -\frac{6}{11} } = \\ = (5\sqrt[6]{5^5 }) ^{ -\frac{6}{11} } = (5\cdot5^{ \frac{5}{6} }) ^{ -\frac{6}{11} } = (5^{ \frac{11}{6} }) ^{ -\frac{6}{11} } =5^{-1}= \frac{1}{5}= 0,2.")