Thanks! It would have been the case if these were first derivatives, but they are second derivatives (would be interesting to try with 1st derivatives and see how it turns out). The geometrical interpretation is a bit tricky to think about:
- if the second derivative is positive, then the function is convex
- if the second derivative is negative, then the function is concave
- if the second derivative is zero (our case), then you might be at some inflection point (where you go from convex to concave or vice versa). But at inflection points, the function itself can have a positive or negative slope, but cannot be at a maximum or minimum (local or global). So really, nothing to obvious that you can spot on the final curve.

Truth is we just needed 2 more equations to complete the system.

If you want to visualise this, I would advise you to go to desmos.com/calculator and plot a function like x^5-2x^3+x and its second derivative, and see for yourself :)