Решите неравенство f' (x) < 0 : 1) f (x) = 2x^4 - x 2) f (x) = 3 x^3 - 27x 3)f(x0 = 1\x...

Question

Решите неравенство f' (x) < 0 :
1) f (x) = 2x^4 - x
2) f (x) = 3 x^3 - 27x
3)f(x0 = 1\x - 2x - 1
4)f (x) = 1\x^2 + 54x + 3
помогите

Answer 1

1) f(x) = 2x^4 - x
f ' (x) = (2x^4 - x) ' = 2*4x^3 - 1 = 8x^3 - 1
8x^3 - 1 ≥ 0
8x^3 ≥ 1
x^3 ≥ 1/8
x ≥ 1/2 = 0,5
x ∈ [ 0,5 ; + беск)

2) f(x) = x^3-27x
f ' (x) = 3x^2 - 27
3x^2 - 27 ≥ 0 / : 3
x^2 - 9 ≥ 0
(x - 3 )(x + 3 ) ≥ 0
x ∈ ( - беск; - 3] ∨ [ 3; + беск)