Answer the Problem $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4 x + 3 , [ - 0.5,1.8 ]$

question 278

Essay

Answer the problem.
-Use the following function and a graphing calculator to answer the questions.
$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4 x + 3 , [ - 0.5,1.8 ]$
a). Plot the function over the interval to see its general behavior there. Sketch the graph below.

b). Find the interior points where f = 0 (you may need to use the numerical equation solver to approximate a solution). You may wish to plot f as well. List the points as ordered pairs (x, y).
c). Find the interior points where f does not exist. List the points as ordered pairs (x, y).
d). Evaluate the function at the endpoints and list these points as ordered pairs (x, y).
e). Find the function's absolute extreme values on the interval and identify where they occur.

---

Definitions:

Vocational Interests

Preferences and inclinations individuals have towards certain professions or career paths.

Personality Psychology

Personality psychology is the study of individual differences in characteristic patterns of thinking, feeling, and behaving.

Organizational

Organizational pertains to the structure and coordination of the activities of a group or entity towards achieving its goals.

Basic Approach

A fundamental strategy or methodology used in a particular field of study or profession, focusing on core principles and techniques.