# Can the line x=0 be differentiable?

1. Apr 27, 2005

### UrbanXrisis

can the line x=0 be differentiable?

the slope would be infinity right? so does that mean it is differentiable?

2. Apr 27, 2005

### cepheid

Staff Emeritus
x = f(y) = 0 is a function, and $\frac{dx}{dy}$ is certainly defined. But graphing that in the traditional manner (indep. variable on the horizontal axis), of course gives a horizontal line of slope 0.

The problem with your example the way you were thinking about it is that it doesn't even represent a function of x! Think about it...you can plug only x = 0 into this "function", and when you do, any conceivable value of y is allowed. Is that a function?

In any case, the slope of a vertical line is undefined.