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.

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Definitions:

Circumduction

A circular movement of a body part, such as a limb, that outlines a cone shape.

Circumduction

A movement that combines flexion, extension, abduction, and adduction in such a way that the distal end of the body part moves in a circle.

Rotation

The act of rotating around an axis or center, often referred to in physics and mechanics, or the movement around a joint in anatomy.

Elevation

An increase in height or the angle of something; also used to describe a geographical area's height above sea level.