Problems 133 – 142. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.

Consider the function

(a) Use a graphing utility to graph f. Determine the turning points on the graph of f .

(b) T he function f(x) = x⁴ − 9x³ + 3x² + 89x − 84 is called the first derivative of f . Find the zeros of f. That is, solve f(x) = 0.

(c) Compare the x -coordinates of the turning points of f to the zeros of f'. What do you notice?

(d) Use a graphing utility to determine the intervals where f is increasing.

(e) T he function ƒ is increasing where f(x) > 0. Use the derivative to determine the intervals for which ƒ is increasing. Because polynomials are continuous over their domain, all endpoints are included in the intervals describing where ƒ is increasing. However, in general, the numbers at the endpoints must be tested separately to determine if they should be included in the intervals describing where a function is increasing or decreasing.

(f) Compare the answers from parts (d) and (e). What do you notice?

Transcribed Image Text:

f(x) = ²⁄²x² − ² / x² + x³ x3 + 4 89 2 x2 - 84x + 1