The absolute minimum value of x^4-x^2-2 x+5

The correct answer is Option 2: is equal to 3

$f(x)=x^4-x^2-2 x+5$

$f'(x) =4 x^3-2 x-2$

$=(x-1)\left(4 x^2+4 x+2\right)$

Clearly at x = 1, we will set the minimum value which is 3.