Finding Points of Inflection

on the TI-89

The point (c, f(c) is a point of inflection if f"(c) = 0 or f"(c) is undefined. It is easy to write a function on the TI-89 (modeled after the critnum() function) that locates values of x where the second derivative equals zero. The function is:

Define ptinf(f, x) = solve(d(f, x, 2) = 0, x)

(If you don't know how to enter a user-defined function into your calculator, click here).

Limitations:

This function only locates points of inflection where f"(x) = 0. You still need to check to see where f"(x) is undefined.

The screen shot at right shows the ptinf() function used to locate points of inflection for the function f(x) = -3x⁵ + 5x³. (Example 4 on p. 183 of the Larsen text).

The right-hand screen shot shows the graph of f in the window -3 < x < 3, -3 < y < 3, with the points of inflection emphasized..

last update October 23, 2003 by JL Stanbrough