Relative Minimums and Maximums of a Polynomial

Front

What are relative minimums and maximums?

Back

Relative minimums and maximums are points on a graph where the function value is lower (minimum) or higher (maximum) than the values of the function at nearby points.

Front

Where do you find relative minimums and maximums?

Back

Turning points of the function.

Front

What is a turning point?

Back

A turning point is a point on the graph of a function where the function changes from increasing to decreasing or from decreasing to increasing.

Front

How can you determine the relative maximum of a polynomial function?

Back

By finding the turning points and evaluating the function at those points.

Front

What is the significance of the first derivative in finding extrema?

Back

The first derivative indicates the slope of the function; where it equals zero, the function may have a relative maximum or minimum.

Front

What does it mean if the second derivative is positive at a turning point?

Back

It indicates that the turning point is a relative minimum.

Front

What does it mean if the second derivative is negative at a turning point?

Back

It indicates that the turning point is a relative maximum.

Front

How do you find the number of extrema in a polynomial function?

Back

By analyzing the degree of the polynomial; a polynomial of degree n can have at most n-1 turning points.

Front

What is the range of a polynomial function?

Back

The set of all possible output values (y-values) of the function.

Front

How do you determine the range of a polynomial function?

Back

By analyzing the behavior of the function as x approaches positive and negative infinity and identifying the minimum and maximum values.