Firstly, to find out the critical points of a function, we must take the derivative of the function.
Given function is f(x) = x^2 - 3x + 2. Let's take its derivative.
The derivative of f(x) = x^2 - 3x + 2 is f'(x) = 2x - 3.
The critical points of a function are the points where the derivative is zero or undefined. In this case, we set f'(x) = 0 to find the x where our function's derivative equals zero.
The equation will be, 2x - 3 = 0.
After adding 3 to both sides to remove 3 from the left side, the equation becomes 2x = 3.
Then, we divide both sides by 2, which yields x = 3/2.
So, the function has only one critical point, which is x = 3/2.
Now, looking at the options given - ["None of those", "-1 and -1", "-1 and -2", "1 and 2", "No critical points"], none of these options include the critical point that we just found (x = 3/2).
Therefore, the correct option is "None of those" as there are no correct options for the critical points of the function f(x) = x^2 - 3x + 2.