Relative Minimums and Maximums of a Polynomial

Front

What is a relative minimum in a polynomial function?

Back

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

Front

What is a relative maximum in a polynomial function?

Back

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

Front

What are turning points in a polynomial function?

Back

Turning points are points on the graph where the function changes direction from increasing to decreasing or vice versa, indicating potential relative maximums or minimums.

Front

How do you find relative maximums and minimums in a polynomial?

Back

Relative maximums and minimums can be found by identifying the turning points of the polynomial, which occur where the first derivative is zero or undefined.

Front

What is the difference between relative and absolute extrema?

Back

Relative extrema are the highest or lowest points in a specific interval, while absolute extrema are the highest or lowest points over the entire domain of the function.

Front

What does the first derivative test indicate?

Back

The first derivative test helps determine whether a critical point is a relative maximum, relative minimum, or neither by analyzing the sign of the derivative before and after the point.

Front

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

Back

The second derivative indicates the concavity of the function; if it is positive at a critical point, the point is a relative minimum, and if negative, it is a relative maximum.

Front

How many extrema can a polynomial function have?

Back

A polynomial function of degree n can have at most n-1 turning points, which means it can have at most n extrema.

Front

What is the y-intercept of a polynomial function?

Back

The y-intercept is the point where the graph of the polynomial crosses the y-axis, found by evaluating the function at x=0.

Front

What is the role of the degree of a polynomial in determining its behavior?

Back

The degree of a polynomial determines the maximum number of turning points and the end behavior of the graph.