local extrema, asymptotes, coordinate intercepts

[Guest gflex200405]

I need to find out where the functions are increasing/decreasing has local extrema where the graph is concave up or concave down, asymptotes and coordinate intercepts. Thanks ahead of time.

 

[bloodhound]

the first ones an "upward" parabola symmetrical around some point c. which also happens to be the global minimum.

 

by increasing do u mean , non decreasing or strictly increasing? my lecturer uses increasing means non decreasing so just want to a clarification

 

if u take the definition to be non decreasing, then basically. f(x) is increasing on (a,b) if f'(x)>=0 for all x in (a,b)

 

(i am not sure about the definition of concave so u might wanna confirm)

f is concave up for some interval if f'' is greater than 0 in that interval

f is concave down if f'' less that 0 in that interval

 

first one and second one dont have asymptotes. to find the coordinate intercepts just see what value f takes when x = 0. and what value x takes when f(x) is 0

 

to find the asymptote to the third one, just see what happens if u increase x bit by bit. lets just increase by 1.

 

f(1)=1/2

f(2)=2/3

f(3)=3/4

 

what do u think will happen to f as x increases indefinitely?

[bloodhound]

note: for the third one , f x is undefined at a certian value of x. giving you another asymptop which in this case is vertical