`f(x) = (x^3 + 5x^2 + 1)/(x^4 + x^3 - x^2 + 2)` Use a computer algebra system to graph `f` and to find `f'`

Textbook Question

Chapter 4, 4.6 - Problem 17 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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tiburtius | High School Teacher | (Level 2) Educator

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We will solve the problem using Wolfram Mathematica (you can also use Wolfram Alpha which is free).

Graph of `f`

Plot[(x^3 + 5 x^2 + 1)/(x^4 + x^3 - x^2 + 2), {x, -10, 10},
PlotRange -> {-1, 8}]

By writing the above line of code we obtain the graph of `f` shown in the image below.

Finding `f'`  

Simplify[D[(x^3 + 5 x^2 + 1)/(x^4 + x^3 - x^2 + 2), x]]

In the code line above command Simplify is there to simplify the result obtained by differentiation.

The result is `f'(x)=(x (-22 - 3 x + 4 x^2 + 6 x^3 + 10 x^4 + x^5))/(2 - x^2 + x^3 + x^4)^2`  

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