Question

So i have to find where the function increases and decreases, rel max and min, concavity and asymptotes for f(x) x+3/x-2

Answer 1

asymptotes are easy, your VA is the bad value for x in the demoniator; x=2

the HA is 0

Answer 2

the 1st and 2nd derivatives will tell you the rest

Answer 3

Function increase is where first derivative > 0
Function decrease is where first derivative < 0
Max is where second derivative = 0 but third derivative < 0
Min is where second derivative = 0 but third derivative > 0

Answer 4

and these are the
first: http://www3.wolframalpha.com/Calculate/MSP/MSP156919f3ef746ifbf4960000527162if13f10i28?MSPStoreType=image/gif&s=38&w=156&h=40
second:
http://www3.wolframalpha.com/Calculate/MSP/MSP10719f3f0ei18e015ch00004ga3ih348bihb16e?MSPStoreType=image/gif&s=18&w=152&h=43
third:
http://www3.wolframalpha.com/Calculate/MSP/MSP43119f3f0a369528375000069i035hd695fi2ef?MSPStoreType=image/gif&s=1&w=164&h=43

derivatives of the given function :)

Answer 5

Shouldn't the HA=1 as both greatest exponents are the same with leading coefficients of 1?