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TGrella
@TGrella
July 2022
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Найдите наименьшее значение функции:
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m11m
Verified answer
X√x=√(x²*x)=√x³ = x^(³/₂)
y'=³/₂ * x^(¹/₂) -6
³/₂ * √x -6=0
3√x - 12=0
√x =4
x=16
При х=2
y=2√2 -6*2 +2000=2√2 + 1988
При x=16
y=16√16 - 6*16 +2000=64 - 96 + 2000=1968 - наименьшее
При х=30
y=30√30 - 6*30+2000=60√7.5 -180+2000=60√7.5 + 1820≈1984.3
Ответ: 1968.
2 votes
Thanks 0
dasdasfa
Y=x√x-6x+2000; x⊂[2;30]
D(y)=[0;+∞)
y'=(x√x) -6x+2000)'= (x^(3/2) )'-6=(3/2)*x^(1/2)-6; y'=0; 1,5√x -6=0; √x=4;x=+-2;
-2∉[2;30]
f(2)=2*√2 -6*2+2000=2√2-12+2000=1988+2√2≈1988+2,8=1990,8;-наименьш
f(30)=30√30 -6*30+2000=1820 +30√30≈1820+30*5,4=1820+162=1982
1 votes
Thanks 0
dasdasfa
извините! не так! корень из х=4; тогда х=16; f(16)=16*4--96+2000=64-96+2000=1968; f(
dasdasfa
f(2)=1990,8; f(30)=1982. f(16)-наименьшее
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Answers & Comments
Verified answer
X√x=√(x²*x)=√x³ = x^(³/₂)y'=³/₂ * x^(¹/₂) -6
³/₂ * √x -6=0
3√x - 12=0
√x =4
x=16
При х=2
y=2√2 -6*2 +2000=2√2 + 1988
При x=16
y=16√16 - 6*16 +2000=64 - 96 + 2000=1968 - наименьшее
При х=30
y=30√30 - 6*30+2000=60√7.5 -180+2000=60√7.5 + 1820≈1984.3
Ответ: 1968.
D(y)=[0;+∞)
y'=(x√x) -6x+2000)'= (x^(3/2) )'-6=(3/2)*x^(1/2)-6; y'=0; 1,5√x -6=0; √x=4;x=+-2;
-2∉[2;30]
f(2)=2*√2 -6*2+2000=2√2-12+2000=1988+2√2≈1988+2,8=1990,8;-наименьш
f(30)=30√30 -6*30+2000=1820 +30√30≈1820+30*5,4=1820+162=1982