Answer:
(-∞, -4] U [1, ∞)
Explanation:
The given function is:
[tex]f(x)=2(x-1)(x+4)^3[/tex]
Since f(x) ≥ 0, we are going to find the range of values of x for which f(x) ≥ 0
By carefully observing the graph shown:
f(x) ≥ 0 for values of x less than or equal to -4, and also for values of x greater than or equal to 1.
This can be written mathematically as:
x ≤ -4 or x ≥ 1
This can be written in interval notation as:
(-∞, -4] U [1, ∞)
