Polynomial Characteristics Check

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What are the characteristics of polynomial functions?

Back

Polynomial functions are continuous, smooth, and can have turning points where the function changes direction.

Front

What is a relative minimum?

Back

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

Front

What is a relative maximum?

Back

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

Front

How do you find the extrema of a polynomial function?

Back

Extrema can be found by identifying the turning points, which occur where the first derivative of the function is zero or undefined.

Front

What is a turning point in a polynomial function?

Back

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

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function value at the second point is greater than the function value at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the function value at the second point is less than the function value at the first point.

Front

What is the significance of the first derivative in polynomial functions?

Back

The first derivative indicates the slope of the function and helps identify intervals of increase and decrease, as well as turning points.

Front

What is the significance of the second derivative in polynomial functions?

Back

The second derivative indicates the concavity of the function and helps determine whether a turning point is a relative maximum or minimum.