# `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'`

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Expert Answers

tiburtius | Certified Educator

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`

Further Reading:

tiburtius | Certified Educator

The image