Final answer:
The smallest zero of the given function is with a multiplicity of 4.
Step-by-step explanation:
The smallest zero of the given function is with a multiplicity of 4.
We can find the zeros of the function by setting it equal to zero and solving for x:
-8(x-1)^(3)(x+2)^(2)x^(4) = 0
From the equation, we can see that each zero has a multiplicity of 1 except for one zero that has a multiplicity of 4.