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