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Igor171717
@Igor171717
July 2022
2
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Построить график функции очень подробно и с разъяснением
y=2/(x^2+4)
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sedinalana
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NNNLLL54
Verified answer
Y=2/(x²+4)
D(y)∈R
y(-x)=2/((-x)²+4)=2/(x²+4) четная
y`=-4x/(x²+4)²=0
x=0
+ _
----------------(0)--------------------
возр max убыв
y(0)=1/2
y``(x)=(-4(x²+4)²-2(x²+4)*2x*(-4x))/(x²+4)^4=-4(x²+4)(x²+4-4x²)/(x²+4)^4=
=-4(x²+4)(4-3x²)/(x²+4)^4=0
4-3x²=0
x=-2/√3 x=2/√3
_ + _
-----------------(-2/√3)--------------------(2/√3)-----------------
выпук вверх вогн вниз выпук вверх
y(-2/√3)=2/(4/3+4)=3/8
y(2/√3)=3/8
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Answers & Comments
Verified answer
Y=2/(x²+4)D(y)∈R
y(-x)=2/((-x)²+4)=2/(x²+4) четная
y`=-4x/(x²+4)²=0
x=0
+ _
----------------(0)--------------------
возр max убыв
y(0)=1/2
y``(x)=(-4(x²+4)²-2(x²+4)*2x*(-4x))/(x²+4)^4=-4(x²+4)(x²+4-4x²)/(x²+4)^4=
=-4(x²+4)(4-3x²)/(x²+4)^4=0
4-3x²=0
x=-2/√3 x=2/√3
_ + _
-----------------(-2/√3)--------------------(2/√3)-----------------
выпук вверх вогн вниз выпук вверх
y(-2/√3)=2/(4/3+4)=3/8
y(2/√3)=3/8