Question

нужна помощь. помогите решить

Answer 1

#19:
$f(x) = x^4 - 4x^2 + 3 \ f'(x) = 4x^3 - 8x = 4x(x^2 - 2)\ f'(x) = 0 textless = textgreater x = 0$ ∪ $x = sqrt2$ ∪ $x = -sqrt2$
f(x)↓ (-∞; -√2] ∪ [0; √2]
f(x)↑ [-√2; 0] ∪ [√2; +∞)
max f(x) = 3
min f(x) = -1
#21:
$left { {{x - y = 8} atop {2^{x - 3y} = 16}} right. textless = textgreater left { {{x = 8 + y} atop {2 ^ {8 - 2y} = 2^4}} right. textless = textgreater left { {{x = 8 + y} atop {2y = 4}} right. textless = textgreater left { {{y=2} atop {x=10}} right.$
#22:
a) $4sin^2(x) = cos(x - frac{ pi }{2}) textless = textgreater 4sin^2(x) = sin(x) textless = textgreater \ sin(x)(4sin(x)- 1) = 0 textless = textgreater$  $sin(x) = 0$ ∪ $sin(x) = frac{1}{4}$
$textless = textgreater x = pi k, k$ ∈ Z ∪ $x = +- arcsin(frac{1}{4}) + 2pi k, k$ ∈ Z
b) {2π; 2π + arcsin(1/4)}