1)y' = 4x³-4x = 4x(x² - 1) = 4x(x-1)(x+1)
2)
[-2][-1][0][1]
3)y(-2) = 16-8+7 = 15, max
y(-1) = 1-2+7 = 6, min
y(0) = 7
Объяснение:
y=x⁴-2x²+7 [-2;0]
y'=(x⁴-2x²+7)'=0
4x³-4x=0 |÷4
x³-x=0
x*(x²-1)=0
x*(x-1)*(x+1)=0
x₁=0 x₂=-1 x₃=1 ∉
y(-2)=(-2)⁴-2*(-2)²+7=16-8+7=15=yнайб.
y(-1)=(-1)⁴-2(-1)²+7=1-2+7=6=yнайм.
y(0)=0⁴-2*0²+7=7
1)y' = 4x³-4x = 4x(x² - 1) = 4x(x-1)(x+1)
2)
[-2][-1][0][1]
3)y(-2) = 16-8+7 = 15, max
y(-1) = 1-2+7 = 6, min
y(0) = 7
Объяснение:
y=x⁴-2x²+7 [-2;0]
y'=(x⁴-2x²+7)'=0
4x³-4x=0 |÷4
x³-x=0
x*(x²-1)=0
x*(x-1)*(x+1)=0
x₁=0 x₂=-1 x₃=1 ∉
y(-2)=(-2)⁴-2*(-2)²+7=16-8+7=15=yнайб.
y(-1)=(-1)⁴-2(-1)²+7=1-2+7=6=yнайм.
y(0)=0⁴-2*0²+7=7