# How do you graph #3x^4-5x^3+x^2-5x-2# by finding all of its roots?

##### 1 Answer

Well, this one is quite tough...or at least for me it is!

I started using Ruffini's Method to reduce the degree of the equation and find the roots:

Where the roots are my intercepts with the

The

When

Then I evaluated the Derivatives:

First Derivative:

Setting this one equal to zero should give me the points of minimum/maximum of my function.

This is not an easy task but using the cubic formula I got that:

I used the following to solve the cubic:

(Reference: http://en.wikipedia.org/wiki/Cubic_function)

Second Derivative:

Setting this one equal to zero should give me the points of inflection of my function. These are for:

Finally your graph: