4) y=x^(2/3)-4x
y' = (2/3)x^(-1/3) - 4
5) y=cos(x)/x
y' = (-xsin(x)-cos(x))/x^2
6) y=sqrt(x)*sin(x)
y' = (1/2)(x^(-1/2))(sin(x)) + sqrt(x)cos(x)
Уравнение y'=0y=6x^2+2x
y' = 12x + 2
12x + 2 = x = -1/6
Неравенство y'>0y=1/5x^5-5/3x^3+6x
y' = x^4 - 5x^2 + y'=0 при x=1, x=-1, x=2, x=-2
Таблица знаковx < -2, y'>-2 < x < -1, y'<-1 < x < 1, y'>x > 1, y'>0
Уравнение y'>0y=-4sin(x)+2x
y' = -4cos(x) + 2
-4cos(x) + 2 = cos(x) = 1/x = π/3 + 2πk, x = 5π/3 + 2πk, k∈Z
4) y=x^(2/3)-4x
y' = (2/3)x^(-1/3) - 4
5) y=cos(x)/x
y' = (-xsin(x)-cos(x))/x^2
6) y=sqrt(x)*sin(x)
y' = (1/2)(x^(-1/2))(sin(x)) + sqrt(x)cos(x)
Уравнение y'=0
y=6x^2+2x
y' = 12x + 2
12x + 2 =
x = -1/6
Неравенство y'>0
y=1/5x^5-5/3x^3+6x
y' = x^4 - 5x^2 +
y'=0 при x=1, x=-1, x=2, x=-2
Таблица знаков
x < -2, y'>
-2 < x < -1, y'<
-1 < x < 1, y'>
x > 1, y'>0
Уравнение y'>0
y=-4sin(x)+2x
y' = -4cos(x) + 2
-4cos(x) + 2 =
cos(x) = 1/
x = π/3 + 2πk, x = 5π/3 + 2πk, k∈Z