Algebra> Find the intervals in which f(x) = jx??2j...

Find the intervals in which f(x) = jx??2j x2 is strictly increasing and strictly decreasing.

reddeiah , 11 Years ago

Grade upto college level

4 Answers

bharat bajaj

Last Activity: 11 Years ago

Please post the questain again. We could not understand your question.
Thanks

Bharat Bajaj

askIITians Faculty

Qualification.

IIT Delhi

Approved

sudhir pal

Last Activity: 11 Years ago

your expression is not so clear so I take the liberty to interpret it in my way

f(x) = |x²|x²

Since x²is always greater than 0 so mod of x²is always positive

So f(x) becomes x⁴

which is decreasing when x<0 and increasing when x>0

Thanks & Regards

Sudhir,

askIITians Faculty

Qualification.

IIT Delhi

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Sher Mohammad

Last Activity: 11 Years ago

Sher Mohammad,

IIT Delhi, B.Tech

Sher Mohammad

Last Activity: 11 Years ago

f(x)=|x-2|/x^2 for x>2=2-x/x^2 for x<2
f'(x)=(4/x^3)-(1/x^2) for x>2
=-((4/x^3)-(1/x^2)) for x<2
for strictly increasing f'(x)>0
(4/x^3)-(1/x^2) >0 for x>2
x>4 for x>2 imply 2<x<4
-((4/x^3)-(1/x^2)) >0 for x<2
1/x^2<-4/x^3 for x<0 imply x<-4
for strictly decreasing f'(x)<0
(4/x^3)-(1/x^2) <0 for x>2
x<4 for x>2 imply x>4
-((4/x^3)-(1/x^2)) <0 for x<2
1/x^2<-4/x^3 for x<2 imply -4<x<2

Sher Mohammad
B.Tech, IIT Delhi.