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What is the least possible value for (x+1)(x+2)(x+3)(x+4)+2019 where x is a real number?

 Feb 25, 2019
 #1
avatar+18458 
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Something is deleted.

 Feb 25, 2019
edited by ElectricPavlov  Feb 26, 2019
 #2
avatar+101871 
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We can answer this with Calculus....but a graph seems better : https://www.desmos.com/calculator/pacud9kcer

 

We have two x values that minimize  (x + 1) (x + 2) (x + 3) ( x + 4)

 

They are 

 

x ≈ -3.618    and   x ≈ -1.382

 

And the minimum value is y = -1

 

So....these  x values also minimize   (x+ 1) (x + 2) ( x + 3) (x + 4) + 2019   =  -1 + 2019 = 2018 

 

 

cool coolcool

 Feb 26, 2019

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