# Thread: Find out all the existing maximum and minimum in the following functions

1. ## Find out all the existing maximum and minimum in the following functions

Hi, I am having difficulty solving a few of these maximum/minimum equations and would appreciate any help given!

f(x)= 1/(x-1), x ∈ R

and it says, note that R is the set of all real numbers.

If maybe you could explain to me what the thought process is so solving this, then I could do the rest myself.

Any help is much appreciated

Regards

Kam

2. a necessary (but not sufficient) condition for f to have a local maximum or minimum at a, is that f'(a) = 0.

in the case at hand, f'(x) = 1/(x-1)^2, which is never 0. so if f has a maximum or minimum, it must be global.

if ±infinity doesn't count, f has no minimum. f(x) gets very small as |x| gets large, but it is never 0. it has a horizontal asymptote (the x-axis).

f(x) is unbounded in any neighborhood of 1, and undefined at 1, it has a vertical asymptote at x = 1.

if we changed variables, by letting u = x-1, f(u) = 1/u. so the graph of f looks just like the graph of g(x) = 1/x, but "shifted right by 1".

3. wow, thank you for the explanation, although that was greek to me! is what you have shown me the actual answer or a general explanation of how max/mins work?

I thought the answer was supposed to be something like x=0 or something like that, i have no idea where you supposed to get f'(a) and u and g(x) from?

Sorry im trying to understand, iv only been presented with this sort of maths yesterday and i have my assignment in for a couple days time! dont know how they expect us to understand this...

im really stuck now! :/ could you possibly show me how you would answer the question and then i could understand things better?

regards

Kam

4. Originally Posted by simagen
wow, thank you for the explanation, although that was greek to me! is what you have shown me the actual answer or a general explanation of how max/mins work?

I thought the answer was supposed to be something like x=0 or something like that, i have no idea where you supposed to get f'(a) and u and g(x) from?

Sorry im trying to understand, iv only been presented with this sort of maths yesterday and i have my assignment in for a couple days time! dont know how they expect us to understand this...

im really stuck now! :/ could you possibly show me how you would answer the question and then i could understand things better?

regards

Kam
What course is this for?

CB