Only (-2, 2) stays below the x-axis, making it the negative interval and the correct option is D.
The graph shows the function f(x) = -x³ + 2x². We can see that the graph is negative between the points x = -2 and x = 2. This means that for any input value x between -2 and 2, the output value f(x) will be negative.
Therefore, the interval (-2, 2) is the only interval listed where the graph is consistently below the x-axis, making it the only negative interval.
Here's a breakdown of the other intervals:
A. (-2, ∞): The graph is negative between -2 and 2, but then it becomes positive after x = 2. So, this is not a completely negative interval.
B. (2, ∞): The graph is positive throughout this interval.
C. (0, 2): The graph is negative between 0 and 2, but it is positive between -2 and 0. So, this is not a completely negative interval.
Therefore, the only interval where the function is consistently negative is (-2, 2) and the correct option is D.