April 21st, 2012, 11:54 PM  #1 
Newbie Joined: Apr 2012 Posts: 18 Thanks: 0  minimum value of function
The minimum value of f(x)=x^8+x^6x^42x^3x^22x+9 is: a 5 b)1 c)0 d)9 
April 22nd, 2012, 12:15 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: minimum value of function
If im not misunderstanding you, then the answer is d) , 9

April 22nd, 2012, 12:22 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs  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. 
April 22nd, 2012, 12:25 AM  #4  
Newbie Joined: Apr 2012 Posts: 18 Thanks: 0  Re: minimum value of function Quote:
 
April 22nd, 2012, 12:39 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs  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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