sketch a polynomial function that has the following properties: a fifth-degree function with 4 zeros, 2 max and 2 min.

Question

please explain, because this is very difficult for me, and I want to be able to figure out other problems like this.

Answer 1

An odd function (fifth degree) will end with the left tail continuing to negative infinity and the right tail continuing to infinity.

The max amount of turns a polynomial can have is n-1

in this case 5-1= 4. So two of your turns will be your relative maximum points ( on the positive side of y)and two of your points will be relative minimums (on the negative side of y).

In order to have 4 zeros you will have 3 zeros crossing the x axis and one zero will be tangent with the x axis.

Think “MW” when drawing the graph.