Finding critical values of a function

[shanshan]

Homework Statement

Use Newton's Method to find the critical numbers of the function f(x) = 2x^5 - 5x^2 - 20x + 12 correct to three decimal places

Homework Equations

The Attempt at a Solution

f'(x) = 10x^4-10x-20
= 10(x^4-x-2)
= 10(x+1)(x^3-x^2+x-2)

I'm not really sure what Newton's method is, so I just tried factoring the derivative, but I can't factor it any further and I don't know what to do from here. HELP!

 

[snipez90]

Wikipedia is your friend:

http://en.wikipedia.org/wiki/Newton's_method

Well you clearly have one critical point which you don't have to estimate. As for the x^3 - x^2 + x - 2 factor, the discriminant of this is negative, and you have two complex roots and a real root. You can disregard the complex roots. If g(x) = x^3 - x^2 + x - 2, then f(1) = -1 and g(2) = 4, which implies that the remaining real root is between x = 1 and x = 2. Now see if you can garner any useful information for approximating this root from the wikipedia article.