1) y = 5 - 3lnx, x₀ = 4
y` = - 3/x
y`(4) = - 3/4
2) y = x³/2 - ln(2x), x₀ = 2
y` = (3x²)/2 - 2/(2x) = (3x²)/2 - 1/x
y`(2) = (3*4)/2 - 1/2 = 11/2 = 5,5
3) f(x) = 6cos(π/3 - 3x) = 6cos(3x - π/3), x₀ = π/6
f1(x) = - 18sin(3x - π/3)
f`(π/6) = - 18sin(3*π/6 - π/3) = - 18sin(π/2 - π/3) = - 18sin(π/6) = - 18*(1/2) = - 9
3^(x + 1) - 3^x = 18
3*(3^x) - 3^x = 18
2*(3^x) = 18
3^x = 9
3^x = 3^2
x = 2
Х+1=0;х+7=0;х-9=0;
х=-1; х=-7; х=9;
Ответ:-7;-1;9
(x+7)-(3x+5)=2
x+7-3x-5=2
-2x=2-7+5
-2x=0
x=0
1) 1/3х(х+1) ≤ (х-1)²
1/3*x(x+1)-(x-1)(x+1)≤0
(x-1)*(1/3*x-x-1)≤0
(x-1)(2/3*x+1)≥0
x=1 x=-1,5
x∈(-∞;-1,5] U [1;∞)
2)1/3х - 4/9 ≥ х(х-1)
x²-x-1/3*x+4/9≤0
x²-4/3*x+4/9≤0
9x²-12x+4≤0
(3x-2)²≤0
3x=2
x=2/3
3)2х-2,5 > х(х-1)
x²-x-2x+2,5<0
x²-3x+2,5<0
D=9-10=-1<0
нет решения