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Find the intervals in which f (x) = |x-2| x2 is strictly increasing and strictly decreasing.

Find the intervals in which f (x) = |x-2| x2 is strictly increasing and strictly decreasing.

Grade:12

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student

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
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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