Suppose the derivative of a function $f$ is \[ f^{\prime}(x)=(x+2)(x-4)^{2}(x-1)^{3} . \] Then $f(x)$ is decreasing on the following interval: $(1, \infty)$ $(-\infty, 1)$ $(1,4)$ $(-\infty,-2)$ $(-2,1)$

Step 1 ：Given the derivative of a function $f$ is $f^{\prime}(x)=(x+2)(x-4)^{2}(x-1)^{3}$.

Step 2 ：The function $f(x)$ is decreasing where its derivative $f'(x)$ is negative. The derivative is a product of several factors, and it will be negative where an odd number of these factors are negative.

Step 3 ：We can find the intervals where each factor is negative, and then combine these intervals to find where the product is negative.

Step 4 ：The roots of the derivative are -2, 1, and 4.

Step 5 ：By analyzing the sign of each factor in the intervals determined by these roots, we find that the derivative is negative in the interval (-2, 1).

Step 6 ：Thus, the function $f(x)$ is decreasing on the interval $\boxed{(-2,1)}$.