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bilenko2001
@bilenko2001
July 2022
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Найдите наименьшее и наибольшее значение функции y= (1-x^2)(x-1) на отрезке [0;2]
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sangers1959
Verified answer
Y=x-x³-1+x²=-x³+x²+x-1 [0;2]
y`=-3x²+2x+1=0
-3x²+2x+1=0 |×(-1)
3x²-2x-1=0 D=16
x=1 x=-1/3 ∉
y(0)=-0³+0²+0-1=-1.
y(1)=-1³+1²+1-1=0=ymax.
y(2)=-2³+2²+2-1=-8+4+2-1=-3=ymin.
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Answers & Comments
Verified answer
Y=x-x³-1+x²=-x³+x²+x-1 [0;2]y`=-3x²+2x+1=0
-3x²+2x+1=0 |×(-1)
3x²-2x-1=0 D=16
x=1 x=-1/3 ∉
y(0)=-0³+0²+0-1=-1.
y(1)=-1³+1²+1-1=0=ymax.
y(2)=-2³+2²+2-1=-8+4+2-1=-3=ymin.