Use the Following Function and a Graphing Calculator to Answer $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } + 3 x + 2 , [ - 0.5,1.8 ]$

question 63

Essay

Use the following function and a graphing calculator to answer the questions.
$f ( x ) = x ^ { 4 } - 4 x ^ { 2 } + 3 x + 2 , [ - 0.5,1.8 ]$
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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