To find the points where the function has a vertical tangent line, we need to find the values of x where the derivative of the function is undefined or infinite.

First, let’s find the derivative of the function F(x) = √(x^2 - x).

Using the chain rule, we have:

F’(x) = (1/2)(x^2 - x)^(-1/2)(2x - 1)

Simplifying this expression, we have:

F’(x) = (x - 1)/(2√(x^2 - x))

To find the values of x where the derivative is undefined or infinite, we set the denominator equal to zero:

2√(x^2 - x) = 0

√(x^2 - x) = 0

Squaring both sides, we have:

x^2 - x = 0

Factoring out x, we have:

x(x - 1) = 0

Setting each factor equal to zero, we have two possible values for x:

x = 0 and x = 1

Therefore, the function F(x) = √(x^2 - x) has vertical tangent lines at x = 0 and x = 1.