Let x be the number of widgets that a factory produces, in millions of widgets.

Let x be the number of widgets that a factory produces, in millions of widgets. Let P represent the profit, in millions of dollars, from selling widgets.
It is known that P is a function of x and that
P(x) = ‐  x2 + x ‐ 2
200
It is also known that difficult regulatory laws and higher taxes become a factor if the profit is more than $39 million.
In this task, you will use different kinds of technology to determine how many widgets should be produced in order to keep profit at $39 million.
A.  Find the exact answer to the scenario using a computer algebra system.
1.  Provide a screenshot, showing your result in the computer algebra system.
Note: The computer algebra system found at the “Wolfram Alpha” web link may be used.
B.  Explain in detail how to use a different technology, without using a computer algebra system, to find the approximation to at least three decimal places for the answer to the scenario’s problem.
1.  Provide an image, showing the final result of part B.
Note: Your explanation must be detailed enough for a novice to accurately follow.
C.  Explain (suggested length of 2 paragraphs) how using both technologies from part A and part B in conjunction with each other in the same secondary mathematics lesson may deepen student understanding of algebra. Include supporting examples in your explanation.
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