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.

 

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?

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