Stationary Point - Possible Values

[BAH0003]

Homework Statement

Hi,

I am having trouble with part d) of this question. It follows on with other parts of a question which I have attached. I have written that 'p' can indeed have stationary points but am not sure what the possible values of 'p' could be. If anyone can list these possible values that would be great, as this is apart of a big assignment that is due soon. Please note this is from question 4 from the first picture.

Thank You and Kind Regards.

Relevant Equations

Please refer to the sheet attatched

Please refer to the image attached

 

[haruspex]

I have written that 'p' can indeed have stationary points but am not sure what the possible values of 'p' could be.

'p' does not have stationary points. It is the number of stationary points that the quartic has.
Think about the derivative of the quartic.