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

Guest Feb 25, 2019

#2**+2 **

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

CPhill Feb 26, 2019