(a) For the function in Exercise 19, find the average of the critical numbers.

(b) For the function in Exercise 19, use a graphing calculator to find the roots of the function, and then find the average of those roots.
(c) Compare your answers to parts (a) and (b). What do you notice?
(d) Repeat part (a) for the function in Exercise 21.
(e) Repeat part (b) for the function in Exercise 21.
(f) Compare your answers to parts (d) and (e). What do you notice? It can be shown that the average of the roots of a polynomial (including the complex roots, if there are any) and the critical numbers of a polynomial (including complex roots of ƒ′(x) = 0, if there are any) are always equal.

Data from Exercise 19

For each function find

Transcribed Image Text:

f(x) 2 3 x - x² - 24x - 4