Hi Holly.

Knowing value of x, we can always find the value of dy/dx from dy/dx = x/(x-2), so that answer option 4 is not valid.

All we have to do is to find the three values of dy/dx.

At x = 0, we have dy/dx = 0, which allows to eliminate option 2 that says "undefined" for dy/dx value at x = 0.

At x = 0.5, dy/dx = 0.5/(-1.5) = -1/3, making option 1 the only correct answer.

At x = 2, we have 0 in denominator of dy/dx expression, so that dy/dx is undefined at x = 2, in accordance to option 1.

Answer: 1).