![y=-2x^2 \\\\ y'=-4x \\\\ -4x=0 \\\\ x=0 \\\\\\\\ y(-3)=-2*(-3)^2=-18 \\\\ y(-1)=-2*(-1)^2=-2](https://tex.z-dn.net/?f=y%3D-2x%5E2+%5C%5C%5C%5C+y%27%3D-4x+%5C%5C%5C%5C+-4x%3D0+%5C%5C%5C%5C+x%3D0+%5C%5C%5C%5C%5C%5C%5C%5C+y%28-3%29%3D-2%2A%28-3%29%5E2%3D-18+%5C%5C%5C%5C+y%28-1%29%3D-2%2A%28-1%29%5E2%3D-2)
<span>наибольшее значение функции - y(-1)=-2
</span>наименьшее значение функции - y(-3)=-18
1) 4x² - 3x + 7 = 2x² + x + 7
4x² - 3x + 7 - 2x² - x - 7 = 0
2x² - 4x = 0
x² - 2x = 0
x(x - 2) = 0
x₁ = 0
x - 2 = 0
x₂ = 2
Ответ : 0 ; 2
2) 10 - 3x² = x² + 10 - x
10 - 3x² - x² - 10 + x = 0
- 4x² + x = 0
4x² - x = 0
x(4x - 1) = 0
x₁ = 0
4x - 1 = 0
4x = 1
x₂ = 0,25
Ответ : 0 ; 0,25
3) (x + 3)(x - 4) = - 12
x² - 4x + 3x - 12 + 12 = 0
x² - x = 0
x(x - 1) = 0
x₁ = 0
x - 1 = 0
x₂ = 1
Ответ : 0 ; 1
4) x² - 1 = 2(x² - 3)
x² - 1 = 2x² - 6
x² - 1 - 2x² + 6 = 0
- x² + 5 = 0
x² - 5 = 0
(x - √5)(x + √5) = 0
x - √5 = 0
x₁ = √5
x + √5 = 0
x₂ = - √5
Ответ : - √5 ; √5
5) x² + 6x = 0
x(x + 6) = 0
x₁ = 0
x + 6 = 0
x₂ = - 6
Ответ : - 6 ; 0
6) x² - 49 = 0
(x - 7)(x + 7) = 0
x - 7 = 0
x₁ = 7
x + 7 = 0
x₂ = - 7
Ответ : - 7 ; 7
4х3-4=0
4х3=4
х3=1
х=1
Ответ. х=1
Точки называются не кризисными, а критическими.
![f(x)=x\cdot sinx+cosx\\\\f'(x)=sinx+x\cdot cosx-sinx=x\cdot cosx=0\\\\1)\; x=0,\\\\2)\; cosx=0,\; x=\frac{\pi}{2}+\pi n,\; n\in Z](https://tex.z-dn.net/?f=f%28x%29%3Dx%5Ccdot+sinx%2Bcosx%5C%5C%5C%5Cf%27%28x%29%3Dsinx%2Bx%5Ccdot+cosx-sinx%3Dx%5Ccdot+cosx%3D0%5C%5C%5C%5C1%29%5C%3B+x%3D0%2C%5C%5C%5C%5C2%29%5C%3B+cosx%3D0%2C%5C%3B+x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%2B%5Cpi+n%2C%5C%3B+n%5Cin+Z)