To find the maximum value of the function 1/(x^2 - 3x + 2), we need to determine the critical points of the function and then evaluate the function at those critical points.

1. Finding the critical points:
To find the critical points, we need to find the values of x where the derivative of the function is equal to zero or undefined. The derivative of the given function is given by:
f'(x) = (-2x + 3)/(x^2 - 3x + 2)^2

Setting f'(x) equal to zero and solving for x:
(-2x + 3)/(x^2 - 3x + 2)^2 = 0

Since the numerator can never be equal to zero, the only way for the fraction to be zero is if the denominator is equal to zero. Thus, we need to solve the equation:
x^2 - 3x + 2 = 0

Factoring this quadratic equation, we get:
(x - 1)(x - 2) = 0

Setting each factor equal to zero, we find two critical points:
x - 1 = 0 => x = 1
x - 2 = 0 => x = 2

2. Evaluating the function at the critical points:
We substitute the critical points into the original function to find the corresponding y-values:
f(1) = 1/(1^2 - 3(1) + 2) = 1/0 (undefined)
f(2) = 1/(2^2 - 3(2) + 2) = 1/0 (undefined)

Since the function is undefined at both critical points, there is no maximum value for the given function.

Therefore, the correct answer is option 'D' (None of these).