I tried this question and made the same mistake as you the first time.

I read the question again and the question asks for the coordinates of the stationary points on the graph of its gradient function (and NOT the stationary points on the graph of y). These are two different things altogether. Stationary points of y and stationary points of the gradient function are NOT the same thing.

Here, what you will first need to do is to find the gradient function dy/dx (which should be 0.25x4 - 3.5x2 + 6x).

The question, hereafter, is trying to ask you to find the stationary points of this function 0.25x4 - 3.5x2 + 6x and not the stationary points of the original function.

What you should do here is to define 0.25x4 - 3.5x2 + 6x as a new function y2 (or perhaps, u) and start over again.

So the question basically asks you to do this.

(i) Find the coordinates of the stationary points of the curve u = 0.25x4 - 3.5x2 + 6x (we no longer care about y anymore, even for the coordinates since the question asks for the coordinates of the stationary points on the GRAPH of the GRADIENT FUNCTION, in which the vertical axis lists down values of dy/dx instead of y).

(ii) Determine the nature of each of these stationary points. This means finding (x, u) or (x, dy/dx).

Let me know if you are still confused.