Question

How do you graph `f(x) = x^5-6x^4+9x^3`?

Answer 1

Graph is inserted.

Explanation:

`f=x^3(x-3)^2` = 0, at x = 0, 0, 0, 3 and 3.#

`f'=x^2(x-3)(5x-9)=0, at x = 0, 0, 9/5 and 3.`

`f'=2x(10x^2-36x+27)=0, at x = 0 and 1.8+-sqrt0.52`

Look for all these aspects depicted, in the inserted graph.

As `x to +- oo, f to +-oo`, on the right and left, respectively,

graph{x^3(x-3)^2x^2 [-10, 10, -50, 50]}