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: 12,211 Thanks: 520 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: 12,211 Thanks: 520 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. 

Tags 
function, minimum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
maximum and minimum of a function  Dmath  Calculus  4  March 9th, 2014 06:19 PM 
minimum value of function  MATHEMATICIAN  Calculus  9  August 31st, 2013 10:33 AM 
Inequality with minimum function  Fruit Bowl  Applied Math  0  January 31st, 2013 10:25 AM 
minimum of a function  david hilbert  Complex Analysis  3  January 28th, 2013 02:33 AM 
minimum of function with 2 variables  bertusavius  Calculus  1  October 18th, 2012 03:08 AM 