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February 6th, 2019, 01:29 AM  #1 
Member Joined: Feb 2018 From: Iran Posts: 38 Thanks: 3  Range of function
For which value of a does the interval [0,1/3] completely include the range of the function: f(x)=1/(3x^(4)âˆ’8ax^(3)+12a^(2)+x^(2)+a) 
February 6th, 2019, 12:25 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,730 Thanks: 689 
It is easier to analyze by $3x^48ax^3+12a^2+x^2+a \ge3$


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function, functions, range, ranges 
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