Question

What is the minimum degree of a polynomial function that has an absolute maximum, a relative maximum, and a relative minimum? Explain your reasoning..

Answer 1

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

`f(x)=x^3+2x^2-3x+1`

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.