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yulia199829
@yulia199829
June 2021
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Найдите наименьшее значение функции .
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oganesbagoyan
Verified answer
F(x) =у = -x³ +3x²-3 ; x∈[ -2 ;1].
--------------------------------
min y -->? (минимальное значение функции)
x∈[-2 ,1]
j
y ' =( -x³ +3x²-3 ) ' = -3x² +6x = -3x(x-2);
y ' = 0 ;
-3x(x-2)= 0 ;
[x =0; x =2.
x =2∉[ -2 ;1].
------------------------
f(-2) = -(-2)³ +3*(-2)² -3 =17;
f(1)= -(1)³ +3*(1)² -3 = - 1;
f(0) = -0³ +3*0² -3 = -3.
min f(x) = f(0) =
- 3 .
x∈[-2 ,1]
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Answers & Comments
Verified answer
F(x) =у = -x³ +3x²-3 ; x∈[ -2 ;1].--------------------------------
min y -->? (минимальное значение функции)
x∈[-2 ,1]
j
y ' =( -x³ +3x²-3 ) ' = -3x² +6x = -3x(x-2);
y ' = 0 ;
-3x(x-2)= 0 ;
[x =0; x =2.
x =2∉[ -2 ;1].
------------------------
f(-2) = -(-2)³ +3*(-2)² -3 =17;
f(1)= -(1)³ +3*(1)² -3 = - 1;
f(0) = -0³ +3*0² -3 = -3.
min f(x) = f(0) = - 3 .
x∈[-2 ,1]