Verified answer

Set derivative equal to 0 and solve for x

F(x) = -x^3 - x

F'(x) = -3*x^2 - 1

solve for x with F'(x) = 0

-3*x^2 - 1 = 0

-3*x^2 = 1

3*x^2 = - 1

x^2 = -1/3

x = sqrt[-1/3]

since the argument of the square root is negative there is no minimun or maximum.

Set the first derivative equal to zero to find all max and min values.