Find the intervals in which f(x) is increasing or decreasing: f(x)=xlxl, x E R.

Asked by raginee311 | 31st Aug, 2015, 08:26: AM

Expert Answer:

C o n s i d e r space t h e space g i v e n space f u n c t i o n f open parentheses x close parentheses equals x open vertical bar x close vertical bar comma space w h e r e space x element of R R e w r i t i n g space t h e space a b o v e space f u n c t i o n comma space w e space h a v e comma f open parentheses x close parentheses equals x open parentheses x squared close parentheses to the power of 1 half end exponent D i f f e r e n t i a t i n g space t h e space a b o v e space f u n c t i o n space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma f apostrophe open parentheses x close parentheses equals square root of x squared end root cross times 1 plus x cross times 1 half cross times open parentheses x squared close parentheses to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent cross times open parentheses 2 x close parentheses space space space space space space space space equals square root of x squared end root plus fraction numerator 2 x squared over denominator 2 square root of x squared end root end fraction space space space space space space space space equals square root of x squared end root plus fraction numerator x squared over denominator square root of x squared end root end fraction space space space space space space space space equals fraction numerator 2 x squared over denominator square root of x squared end root end fraction space space space space space space space space equals fraction numerator 2 x squared over denominator open vertical bar x close vertical bar end fraction space space space space space space space space equals 2 open vertical bar x close vertical bar T h u s comma space f apostrophe open parentheses x close parentheses less or equal than 0 comma space i f space x less-than or slanted equal to 0 space a n d space f apostrophe open parentheses x close parentheses greater or equal than 0 comma space i f space x greater or equal than 0 T h e r e f o r e comma space f open parentheses x close parentheses space i s space d e c r e a sin g space i n space t h e space i n t e r v a l space left parenthesis negative infinity comma 0 right square bracket space space a n d space i t space i s space i n c r e a sin g space i n space t h e space i n t e r v a l space left square bracket 0 comma infinity right parenthesis.

Answered by Vimala Ramamurthy | 31st Aug, 2015, 09:34: AM

Concept Videos

Learn and check the techniques of using derivative to find the intervals i...

This video explains the techniques of using derivative to find the interval...

Learn and check the techniques of using derivative to find the intervals in...

Practice Test
All Questions Ask Doubt