100 баллов!!! помогите!!!. Created by afanasevanatal. matematika-ru

100 баллов!!! помогите!!!...

afanasevanatal @afanasevanatal

March 2022 1 38 Report

100 баллов!!! помогите!!!

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IrkaShevko

Verified answer

1)
1. f'(x) = 1/x * (4x³ + √x) + lnx * (12x² + 1/(2√x))
2. f'(x) = ((10x + 6)(6-4x³) - (5x² + 6x)(-12x²))/(6-4x³)² = (-40x⁴ - 24x³ + 60x + 36 + 60x⁴ - 72x³)/(6-4x³)² = (20x⁴ - 96x³ + 60x + 36)/(6-4x³)² = (5x⁴ - 24x³ + 15x + 9)/(3 - 2x³)²
3. f'(x) = -1/sin²x + 8x⁻⁹
4. f'(x) = sin(5²ˣ) * 5²ˣ * ln5

2)
v(t) = S'(t) = 3t² + 10t
a(t) = v'(t) = 6t + 10

v(2) = 12 + 20 = 32
a(2) = 12 + 10 = 22

3)
y' = x - x² = 0
x₁ = 0
x₂ = 1

y(-1) = 1/2 + 1/3 = 5/6 - наибольшее значение
y(0) = 0 - локальный минимум
y(1) = 1/2 - 1/3 = 1/6 - локальный максимум
y(6) = 18 - 72 = -54 - наименьшее значение

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