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amateurmathlover April 21st, 2012 11:54 PM

minimum value of function
 
The minimum value of f(x)=x^8+x^6-x^4-2x^3-x^2-2x+9 is:
a 5
b)1
c)0
d)9

mathbalarka April 22nd, 2012 12:15 AM

Re: minimum value of function
 
If im not misunderstanding you, then the answer is d) , 9

MarkFL April 22nd, 2012 12:22 AM

Re: minimum value of function
 
The derivative of f equated to zero has only 1 real root, which is .

meaning there is a minimum there and since f has an even order, we know this is a global minimum.


amateurmathlover April 22nd, 2012 12:25 AM

Re: minimum value of function
 
Quote:

Originally Posted by MarkFL
The derivative of f equated to zero has only 1 real root, which is .

meaning there is a minimum there and since f has an even order, we know this is a global minimum.


Thanks. The problem I was facing was with finding the roots of the first derivative. Can u please explain how u have found that? Thanks again :D

MarkFL April 22nd, 2012 12:39 AM

Re: minimum value of function
 
I used the rational roots theorem, and checked, using polynomial division to find:



I then found numerically that the remaining 6th order factor has a global minimum greater than zero, hence it has no real roots.


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