Mean Value Theorem:
The Mean Value Theorem states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

Given function:
The given function is f(x) = 1 - x^2 * x^3.

Applying the Mean Value Theorem:
In order to apply the Mean Value Theorem, we need to check if the given function satisfies the conditions of the theorem.

1. Continuity:
The given function f(x) is a polynomial, and polynomials are continuous for all real numbers. Therefore, the function is continuous on the closed interval [-1, 1].

2. Differentiability:
The given function f(x) is a polynomial, and polynomials are differentiable for all real numbers. Therefore, the function is differentiable on the open interval (-1, 1).

Finding the value of x:
Now, we need to find the value of x in the open interval (-1, 1) for which the Mean Value Theorem is satisfied.

Let's find the derivative of the given function:
f'(x) = d/dx (1 - x^2 * x^3)
= -2x^4 - 3x^5

Now, let's find the average rate of change of the function f(x) over the interval [-1, 1]:
(f(1) - f(-1))/(1 - (-1))
= (1 - (1^2 * 1^3)) - (1 - ((-1)^2 * (-1)^3))/(1 - (-1))
= (1 - 1) - (1 - 1)/(1 - (-1))
= 0

According to the Mean Value Theorem, there exists at least one value c in the open interval (-1, 1) such that f'(c) = 0. This means that there exists a value of x in the open interval (-1, 1) for which the derivative of the function is 0.

Finding the value of x:
Let's solve the equation f'(x) = 0 to find the value of x:
-2x^4 - 3x^5 = 0
x^4(2 + 3x) = 0

From this equation, we can see that either x^4 = 0 or (2 + 3x) = 0.

x^4 = 0 gives us x = 0, which is not in the open interval (-1, 1).

(2 + 3x) = 0 gives us x = -2/3.

Therefore, the value of x in the open interval (-1, 1) for which the Mean Value Theorem is satisfied is x = -2/3.

Hence, the correct answer is option 'B' (-2/3).