7.
![f(x)=( \sqrt{x} + \frac{1}{ \sqrt{x} })^{40}=(x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{40}](https://tex.z-dn.net/?f=f%28x%29%3D%28%20%5Csqrt%7Bx%7D%20%2B%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7Bx%7D%20%7D%29%5E%7B40%7D%3D%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B40%7D)
![f'(x)=((x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{40})'=40(x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{39}*( \frac{1}{2}x^{ -\frac{1}{2} }- \frac{1}{2}x^{ -\frac{3}{2} } )=](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B40%7D%29%27%3D40%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B39%7D%2A%28%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D-%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B%20-%5Cfrac%7B3%7D%7B2%7D%20%7D%20%29%3D)
![=20(x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{39}*( x^{ -\frac{1}{2} }- x^{ -\frac{3}{2} } )](https://tex.z-dn.net/?f=%3D20%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B39%7D%2A%28%20x%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D-%20x%5E%7B%20-%5Cfrac%7B3%7D%7B2%7D%20%7D%20%29)
![f'(1)=20(1^{ \frac{1}{2} } +1^{ -\frac{1}{2} })^{39}*( 1^{ -\frac{1}{2} }- 1^{ -\frac{3}{2} } )=0](https://tex.z-dn.net/?f=f%27%281%29%3D20%281%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2B1%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B39%7D%2A%28%201%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D-%201%5E%7B%20-%5Cfrac%7B3%7D%7B2%7D%20%7D%20%29%3D0)
8. f(x)=(x-2)²(x+4)=(x²-4x+4)(x+4)=x³+4x²-4x²-16x+4x+16=x³-12x+16
f'(x)=3x²-12≤0
3x²≤12
x²≤4
x∈[-2;2]
2'=0.
х'=1.
(3х)'=3.
(Х^3)= 3х^2.
(4х^4+4)'=16х^3.
(1/2•х^4+2/3•х^3+2х^2+2)'=2х^3+2х^2+4х.
((3х^3-2)(2х^2-3))'=9х^2•(2х^2-3)+4 х •(3х^3-2).
((3х^2)/(х+2))'=(6х•(х+2)-3х^2)/(х+2)^2=3х/(х+2).
Ответ:
z=-2, m=-2.
Объяснение:
![\\{ {{2-5(0,2m-2z)=3(3z+2)+2m} \atop {4(z-2m)-(2z+m)=2-2(2z+m)}} \right\\](https://tex.z-dn.net/?f=%5C%5C%7B+%7B%7B2-5%280%2C2m-2z%29%3D3%283z%2B2%29%2B2m%7D+%5Catop+%7B4%28z-2m%29-%282z%2Bm%29%3D2-2%282z%2Bm%29%7D%7D+%5Cright%5C%5C)
Разложим действия в скобках:
![\\\{ {{2-m+10z=9z+6+2m} \atop {4z-8m-2z-m=2-4z-2m}} \right.](https://tex.z-dn.net/?f=%5C%5C%5C%7B+%7B%7B2-m%2B10z%3D9z%2B6%2B2m%7D+%5Catop+%7B4z-8m-2z-m%3D2-4z-2m%7D%7D+%5Cright.)
Упростим выражения:
![\\\{ {{-2m-m+10z-9z=6-2} \atop {4z-2z+4z-m-8m+2m=2}} \right.](https://tex.z-dn.net/?f=%5C%5C%5C%7B+%7B%7B-2m-m%2B10z-9z%3D6-2%7D+%5Catop+%7B4z-2z%2B4z-m-8m%2B2m%3D2%7D%7D+%5Cright.)
Вычислим:
![\\\{ {{-3m+z=4} \atop {6z-7m=2}} \right.](https://tex.z-dn.net/?f=%5C%5C%5C%7B+%7B%7B-3m%2Bz%3D4%7D+%5Catop+%7B6z-7m%3D2%7D%7D+%5Cright.)
Выразим из 1-го ур-я z:
z=4+3m
Подставим это выражение в ур-е 2:
6(4+3m)-7m=2
24+18m-7m=2
11m=-22
m=-2
Подставим полученный ответ в наше выражение:
z=4+3(-2)=4-6=-2.
Проверка.
![\\\{ {{2+2+10(-2)=9(-2)+6+2(-2)} \atop {4(-2)-8(-2)-2(-2)+2=2-4(-2)-2(-2)}} \right.](https://tex.z-dn.net/?f=%5C%5C%5C%7B+%7B%7B2%2B2%2B10%28-2%29%3D9%28-2%29%2B6%2B2%28-2%29%7D+%5Catop+%7B4%28-2%29-8%28-2%29-2%28-2%29%2B2%3D2-4%28-2%29-2%28-2%29%7D%7D+%5Cright.)
![\\\{ {{-16=-16} \atop {14=14}} \right.](https://tex.z-dn.net/?f=%5C%5C%5C%7B+%7B%7B-16%3D-16%7D+%5Catop+%7B14%3D14%7D%7D+%5Cright.)
Решение приведено на фото.
Решение смотри на фотографии