Answer
$[-4, -2] U [2, ∞)$
Work Step by Step
$x^3 + 4x^2\geq 4x + 16$
Find the roots of the function
$x^3 + 4x^2 - 4x - 16 \geq 0$
$(x^2 - 4) (x+4) \geq 0$
$(x+4)(x+2)(x-2) \geq 0$
$x = -4, -2, 2$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -4] $(-)(-)(-) = (-)$
[-4, -2] $(+)(-)(-) = (+)$
[-2, 2] $(+)(+)(-) = (-)$
[2, ∞) $(+)(+)(+) = (+)$
Thus the solution is $[-4, -2] U [2, ∞)$
