How do you graph #3x^4-5x^3+x^2-5x-2# by finding all of its roots?
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
Then I evaluated the Derivatives:
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:
Setting this one equal to zero should give me the points of inflection of my function. These are for:
Finally your graph: