Posted by Jake on Saturday, April 14, 2012 at 7:56pm.
Use the algorithm for curve sketching to sketch the graph of each function.
a) f(x) 4x^3+6x^224x2
1. First to find intercepts
y=0
0=4x^3+6x^224x2
=2(2x^3+3x^312x1)
I don't know how to find the xintercept. I can't use quadratic formula or synthetic division :S

Calculus  Reiny, Saturday, April 14, 2012 at 8:27pm
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.

Calculus  Jake, Saturday, April 14, 2012 at 9:15pm
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

Calculus  Reiny, Saturday, April 14, 2012 at 9:36pm
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.
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