Question

What is the least possible degree of the polynomial graphed above?

Answer 1

Using it's critical points, it is found that the least possible degree of the polynomial graphed above is 4.

What are the critical points of a function?

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

At these critical points, the behavior of the function changes from increasing to decreasing or vice versa.

If a function has n critical points, the least possible degree is of n + 1.

From the changes in behavior of the graph, the function has critical points at:

• $x \approx -0.5$.

• $x \approx 2$

• $x \approx 3.5$

The function has 3 critical points, hence the least possible degree of the polynomial graphed above is 4.

You can learn more about critical points at brainly.com/question/2256078