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keklol2015
@keklol2015
July 2022
2
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Решите неравенство F`(x)>-2, если f(x)=1\x
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ПрофиЗнания
F'(x)= -1/x²
-1/x²>-2
-2x²<-1
2x²>1
x²>1/2
x1=√1/2
x2=-√1/2
(-∞;-√1/2)∪(√1/2;+∞)
0 votes
Thanks 0
sedinalana
F(x)=-1/x²
-1/x²>-2
1/x²<2
1/x²-2<0
(1-2x²)/x²<0
(1-√2x)(1+√2x)/x²<0
x=-1/√2 x=1/√2 x=0
_ + + _
-----(-1/√2)-------------(0)-------------(1/√2)----------
x∈(-∞;-1/√2) U (1/√2;∞)
0 votes
Thanks 0
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Answers & Comments
-1/x²>-2
-2x²<-1
2x²>1
x²>1/2
x1=√1/2
x2=-√1/2
(-∞;-√1/2)∪(√1/2;+∞)
-1/x²>-2
1/x²<2
1/x²-2<0
(1-2x²)/x²<0
(1-√2x)(1+√2x)/x²<0
x=-1/√2 x=1/√2 x=0
_ + + _
-----(-1/√2)-------------(0)-------------(1/√2)----------
x∈(-∞;-1/√2) U (1/√2;∞)