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]
X кг-100%
90 кг-10%
x=100×90/10=900
Ответ:900кг
Решение задания приложено
{4х - у = 20
{4х + у =12
8х=32|:8
х=4
у=12-4х
у=12-4*4=12-16
у=-4
{9х+17у=52
{26х-17у=18
35х=70|:35
х=2
17у=52-9х
17у=52-9*2
17у=52-18
17у=34|:17
у=2
{-5х+7у=2|*(-1)
{8х+7у=15
{5х-7у=-2
{8х+7у=15
13х=13|:13
х=1
8*1+7у=15
7у=15-8
7у=7|:7
у=1
{9х-6у=24
{9х+8у=10|*(-1)
{9х-6у=24
{-9х-8у=-10
-14у=14|:(-14)
у=-1
9х-6*(-1)=24
9х=24-6
9х=18|:9
х=2
1)<u> x(x+3) </u><u />=<u> x </u><u />
a(3+x) a
2)<u> b</u>²<u> </u>=<u /><u /><u> b </u><u />
b(b+c) b+c
3)<u /><u> 2(a+2) </u><u />=<u> 2
</u><u /> (a+2)(a-2) a-2
<u />4) <u> (x+y)(x-y) </u>=<u> x+y
</u> x(x-y) x