How do I find the nature of turning points using this function?

Hi all. I was asked to create a function which uses the turning points of a differentiable function in order to find the first derivative which is not equal to zero after which it finds the nature of the turning points given. The code for the function requires a while loop or a for loop. How can this be done please? Thanks in advance

Answer 1

[Walter Roberson]

values that are exactly the same are derivative 0. Once you find a value not equal to the first value, then any string of increases is a positive derivative, any string of decreases is a negative derivative, places you change between runs are turning point.

Hint: diff and sign

[Nico Degabriele]

Hi, thanks for your answer. I understood what u wrote however I am still unsure about how to start the code. I am just not sure as to how to use each separate turning point for the loop. How is this to be done please?