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maksimkap7
@maksimkap7
July 2022
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Помогите срочно нужно!
Найдите наименьшее значение функции y=(x-1)(x-3)^2-3 на отрезке [2;4]
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mikael2
Verified answer
Y=(x-1)(x²-6x+9) -3 =x³-x²-6x²+6x+9x-9-3=x³-7x²+15x -12
x=2 y=8-28+30-12= -2
x= 4 y= 64 -112+60-12 = 0
y ' =3x²-14x+15=0 D=196- 180=16 √D=4
x1=1/6(14+4) = 18/6=3 x2=1/6(14-4) =10/6=5/3
y(3) =27-63+45-12=
-3
y(5/3)=125/27 -7*25/9 +15*5/3-12=125/27-175/9+75/3-12= -1 22/27
наименьшее значение -3
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Answers & Comments
Verified answer
Y=(x-1)(x²-6x+9) -3 =x³-x²-6x²+6x+9x-9-3=x³-7x²+15x -12x=2 y=8-28+30-12= -2
x= 4 y= 64 -112+60-12 = 0
y ' =3x²-14x+15=0 D=196- 180=16 √D=4
x1=1/6(14+4) = 18/6=3 x2=1/6(14-4) =10/6=5/3
y(3) =27-63+45-12= -3
y(5/3)=125/27 -7*25/9 +15*5/3-12=125/27-175/9+75/3-12= -1 22/27
наименьшее значение -3