differentiation stationary points

Find the stationary points of the graph y = 1/x + 1/x^2 + 1/x^3 and determine the nature of each.

I found the derivative which I did -x^-2 - 2x^-3 - 3x^-4 (i know you can write it as a fraction as well) and then I set this equal to 0. I then divided by x^4 on both sides and got -x^2 - 2x - 3 = 0 and I made i divided it by -1 to give me nice positive numbers to work with: x^2 + 2x + 3 = 0
However, this gives me no real solutions when solving for x.

Could someone please explain how to do this question? Thanks in advance

It seems like you don't understand how to differentiate properly yet.
To me it looks like you multiplied the constants by the negative of the powers and then added one to the power and then made it negative?

To differentiate a polynomial like that you take each term and multiple the constant by the power and then take away one from the power.

Can you please post a photo of the original question? That graph doesn't have any stationary points.

The question is exactly the same

No it's not. You wrote this:

y = 1/x + 1/x^2 + 1/x^3

But it's actually this:

y = 1/x + 1/x^2 - 1/x^3

Try the question again with this correction.

The differentiation looks fine to me. Did you read their equation correctly?