Question

Use the algorithm for curve sketching to sketch the graph of each function.

a) f(x) 4x^3+6x^2-24x-2

1. First to find intercepts

y=0

0=4x^3+6x^2-24x-2

=2(2x^3+3x^3-12x-1)

I don't know how to find the x-intercept. I can't use quadratic formula or synthetic division :S

Answer 1

ok, so you would have to solve

4x^3 + 6x^2 - 24x - 2 = 0

I also could not find any "nice" f(x) = 0
(I tried x = ±2, ±1/2)

so I went to the reliable Wolfram to get
http://www.wolframalpha.com/input/?i=4x%5E3+%2B+6x%5E2+-+24x+-+2+%3D+0

notice that all 3 roots appear to be irrational
making it a messy solution.

Answer 2

I checked in the book answer and the site u gave me matched with the answer.

How did the website get solutions as:

x= -3.28183
x= -1.863

Answer 3

There is no simple formula to solve a general cubic equation.
There are several methods that can be used to find solutions ...
- Newton's Method and some type of iteration algorithms are the most popular

once you have one of the roots of the cubic, you can do long division or use synthetic division to reduce the cubic to a quadratic.
From there you can use the quadratic formula to find the other two roots
I don't know what method the Wolfram site uses.