If a functions domain is all real numbers does it have any local extremum?

Question

anonymous · Answer

@amriju

anonymous · Answer

|dw:1351591542290:dw|

anonymous · Answer

this has local min at 0 but no local max

amriju · Answer

is this the graph of the function?

anonymous · Answer

no. there is no function given

anonymous · Answer

this is graph of lxl. just random example

amriju · Answer

it has no maximum...ofcourse...coz u dont have a limit to the range of the function..the graph keeps on increasing endlessly to infinity....had u but put a limit to the range..( or domain)....that wud be the maxima for this graph

amriju · Answer

does the range of mod x has a limit..?...can u see why u dont have a maximum?...the graph just keeps on increasing..u cant say that ...this is the maximum value....unless u fix its domain or range

anonymous · Answer

it just states that the domain is all real numbers

amriju · Answer

It can have an extrema...it also maynot have....depends on function...but u cant say that..
"If a functions domain is all real numbers it can NEVER have any local extremum"

anonymous · Answer

ok thankyou