Let us define the following terms,
1) Absolute maximum : This is the highest point over the entire domain of a function.
2) Relative maximum : This is the highest part of a particular section of a graph.
3) Relative minimum : This is lowest point of a certain section of a graph.
Hence, the minimum degree of a polynomial function that has an absolute maximum, a relative maximum, and a relative minimum is 3- degree polynomial function.
Let us sketch an example of 3- degree polynomial function in order to give it a better explanation.
For example, let us take
[tex]f(x)=x^3+2x^2-3x+1[/tex]Conclusively, the graph shown above, explained the reason why the 3- degree is the minimum polynomial function that has an absolute maximum, a relative maximum, and a relative minimum.
