We want find where x → 21*x^4 + 73*x^3 - 57*x^2 + 73*x - 78 (polynomial of even degree) takes the minimum value by using min0.htm (for the maximun value I can use max0.htm). Suppose we want to know the rounded value to 6 digits. We prove with a = -10 and b = 10, and click "test".
For x → ∞ and for x → −∞ a polynomial function of degree 4 tends to ∞. I understand that min is between -6 (8880) and 2 (760). If I used a program that allows me to draw graphs, for example R (or Desmos), I would get:
Anyway, starting from a = -6, b = 2, I get:
The minimum value is -1087.8428466719... reached when x = -3.1295325..., rounding: -3.12953.
If (for some reason) I needed more digits, I would have to resort to looking for where the first derivative is 0 with a program for the solution of polynomial equations. I find: -3.12953249066755.