1) не знаю, что такое парная функция.
2)3⁴; 27; √81
3) arctg1 = π/4
4) tgx = 1
x = π/4 + πn , n ∈Z
5)√(1 - x) = 4
1 - x = 16
x = -15 ∈(-20;-10)
6) y = Cos3x
y' = -3Sin3x = -3*Sin(3*π/18) = -3*Sinπ/6 = -3/2
7) 1 - B
2 - A
3 - Б
4 - Д
8) f'(x) = ((х+1)/(x -1))' =( (х+1)' *(x -1) - (х+1)*(x -1)' )/(x -1)²=
= (x -1 -x -1)/(x -1)² = -2/(x -1)²
f'(3) = -2/(3 -1)² = -1/2
9) y = (3x +1)³Cos³(x² +2x +1)
y' = ((3x +1)³)' *Cos³(x² +2x +1) + (3x +1)³ *(Cos³(x² +2x +1))'=
= 9(3x +1)² *Cos³(x² +2x +1) +
+ (3x +1)³ * 3Cos²(x² +2x +1) * Sin(x² +2x +1) * (2x +2)
10) y= 4/x + x [1;3]
y' = -4/x² +1 = (x² -4)/x²
(x² -4)/x² = 0
x² -4 = 0, ⇒ x = +-2
a) x = 1
у = 4/1 +1 = 5
б)х = 3
у = 4/3 +1 = 7/3
в)х = 2
у = 4/2 +1 = 3
Ответ: min y = 2
max e = 5
11) y = 2x⁶ -6x²
y' = 12x⁵ -12x
12x⁵ -12x = 0
x(12x⁴ -12 ) = 0
x = 0 или 12x⁴ -12 = 0
x⁴ = 1
x = +-1
-∞ -1 0 1 +∞
- - + + это знаки для "х"
+ - - + это знаки 12x⁴ -12
убывание возр-е убыв-е возр-е