Maths question helppp

I have a differentiated a term and ended up with

x^2+1 all over x^2. I need to work out the turning points or stationary points of this equation. I have equated this to 0 but end up with x^2=-1 which gives me no values what are the turning points?

@RDKGames

original function was x^2-1 all over x. @RDKGames

is this function an injection or surjection? @RDKGames

What do you think? Refer to definitions

Its not an injection if two elements map onto the same element?

so this function will be surjective. So what would the inverse function be and how would you calculate that?

Have you learnt about it?? Just try to employ it here in the exact same fashion.

Have you learnt about it?? Just try to employ it here in the exact same fashion.

I have but i cant remember how to start it

Look at your notes!

Denote $f(x) = x^2 - 6x +3$

Define

$f(0) + f(1) + f(2) + f(3) + \ldots + f(n) = A_0 + A_1 n + A_2 n^2 + \ldots$ (*)

$\implies f(0) + f(1) + f(2) + f(3) + \ldots + f(n+1) = A_0 + A_1 (n+1) + A_2 (n+1)^2 + \ldots$ (**)

Then (**) - (*) means

$f(n+1) = A_1 + A_2[(n+1)^2 - n^2] + A_3 [(n+1)^3 - n^3] + \ldots$

Now compare coefficients.

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How can you compare coefficeints to that?

is the quadratic also know as homogeneous differential equation or is that something else?