Turning Points of a Polynomial Function

Front

What are turning points in a polynomial function?

Back

Turning points are points on the graph of a polynomial where the function changes direction from increasing to decreasing or vice versa.

Front

Where do you find relative minimums and relative maximums?

Back

Turning points.

Front

What is the maximum number of turning points for a 4th degree polynomial?

Back

3 turning points.

Front

How is the maximum number of turning points related to the degree of the polynomial?

Back

The maximum number of turning points is one less than the degree of the polynomial.

Front

What is a relative maximum?

Back

A relative maximum is a point on the graph where the function value is higher than the values of the function at nearby points.

Front

What is a relative minimum?

Back

A relative minimum is a point on the graph where the function value is lower than the values of the function at nearby points.

Front

If a polynomial has a degree of 5, what is the maximum number of turning points it can have?

Back

4 turning points.

Front

What is the significance of turning points in graphing polynomial functions?

Back

Turning points help identify the shape of the graph and the intervals where the function is increasing or decreasing.

Front

How can you determine the turning points of a polynomial function?

Back

By finding the derivative of the function, setting it to zero, and solving for the x-values.

Front

What does it mean if a polynomial has no turning points?

Back

It means the polynomial is either always increasing or always decreasing.