y=x
4
−18x
2
y
′
=4x
3
−36x=4x(x−3)(x+3)=0 , x
1
=0 , x
=−3 , x
=3
znaki y
: −−−(−3)+++(0)−−−(3)+++
↘ (−3) ↗ (0) ↘ (3) ↗
y(x) vozrastaet : x∈[−3 ; 0 ] , \x∈[ 3 ;+∞)
y(x) ybuvaet : x∈(−∞;−3 ] , x∈[ 0 ; 3 ]
![y=x^4-18x^2\\\\y'=4x^3-36x=4x\, (x-3)(x+3)=0\ \ ,\ \ x_1=0\ ,\ x_2=-3\ ,\ x_3=3\\\\znaki\ y'\ :\ \ \ ---(-3)+++(0)---(3)+++\\\\{}\qquad \qquad \qquad \ \, \searrow \ \ (-3)\ \ \nearrow \ \ \, (0)\ \ \searrow \ \ \ (3)\ \ \ \nearrow \\\\y(x)\ vozrastaet\ :\ \ x\in [-3\ ;\ 0\ ]\ ,\ \x\in [\ 3\ ;+\infty \, )\\\\y(x)\ ybuvaet\ :\ \ x\in (-\infty \, ;\, -3\ ]\ ,\ \ x\in [\ 0\ ;\ 3\ ]](/tpl/images/1693/0903/91e02.png)
