The derivatives of a fourth degree polynomial may help us divulge the curve's shape. We may focus on various regions by calculating values of f, f ' and f ''. What numbers do we use for x? An answer is found by finding the zeros of the function, the zeros of the first derivative and the zeros of the second derivative augmented by taking some number between each of these zeros and by looking at f(x) as x goes to negative or positive infinity. Then we construct a table and give conclusions based on each of the calculations.
Interesting Polynomial Points In: Region A may look like it contains only one zero of this function but it does not!
Region B has a zero of this function. Can you find it?
Region C contains a point where the curve goes across it's tangent line.
Region D has a point of f(x) that is way down low. How low?
4th Degree Polynomial
