Derivative of a Polynomial Function

App Controls

In the app adjust the coefficients to obtain a polynomial function of degree 0-8, Adjust the graphing window with the controls in the app. Use the checkboxes to see the graph of the original polynomial function and/or its first three derivatives, along with interesting points.

Polynomial Characteristics

All polynomial functions are continuous and smooth over their domain, which is the set of all real numbers. It has no holes, vertical or horizontal asymptotes, or sharp corners. A polynomial function of degree n has at most n x-intercepts, n-1 local extrema, and n-2 inflection points. The leading coefficient determines the direction on the far right with the arrow going up when the leading coefficient is positive and going down if he leading coefficient is negative. These arrows point the same way when n is even and opposite directions when n is odd. The extrema of the original function occur at x-values where the first derivative is zero. The inflection points of the original function occur at x-values where the second derivative is zero.