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ГОСТЬ2014
@ГОСТЬ2014
August 2022
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помогите с 5 и 6. определите промежутки монотонности функции
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sedinalana
Verified answer
5
f(x)=4√x*(2-x)
D(f)∈[0;∞)
f`(x)=2(2-x)/√x-4√x=(4-2x-4x)/√x=(4-6x)/√x=0
4-6x=0
6x=4
x=2/3
+ _
[0]--------------------(2/3)---------------------
возр убыв
6
f(x)=4√(x+1)*(3-x)
D(f)∈[-1;∞)
f`(x)=2(3-x)/√(x+1)-4√(x+1)=(6-2x-4x-4)/√(x+1)=(2-6x)/√(x+1)=0
2-6x=0
6x=2
x=1/3
+ _
[-1]-------------(1/3)-----------------
возр убыв
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Answers & Comments
Verified answer
5f(x)=4√x*(2-x)
D(f)∈[0;∞)
f`(x)=2(2-x)/√x-4√x=(4-2x-4x)/√x=(4-6x)/√x=0
4-6x=0
6x=4
x=2/3
+ _
[0]--------------------(2/3)---------------------
возр убыв
6
f(x)=4√(x+1)*(3-x)
D(f)∈[-1;∞)
f`(x)=2(3-x)/√(x+1)-4√(x+1)=(6-2x-4x-4)/√(x+1)=(2-6x)/√(x+1)=0
2-6x=0
6x=2
x=1/3
+ _
[-1]-------------(1/3)-----------------
возр убыв