- #1
UrbanXrisis
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can the line x=0 be differentiable?
the slope would be infinity right? so does that mean it is differentiable?
the slope would be infinity right? so does that mean it is differentiable?
Yes, a vertical line can be differentiable at a point if the derivative at that point exists. However, the derivative of a vertical line is undefined because the slope of a vertical line is infinite.
No, the line x=0 is not differentiable at all points. It is only differentiable at the point (0,0) because the derivative at any other point would be undefined.
Yes, the line x=0 can have a continuous derivative at the point (0,0). This means that the left and right derivatives at that point are equal.
The geometric interpretation of the derivative of a vertical line is the slope of the tangent line at a specific point on the line. Since the slope of a vertical line is undefined, the derivative at that point does not exist.
Yes, a function can be differentiable even if the line x=0 is not differentiable. The differentiability of a function depends on the behavior of the function, not just on the differentiability of individual lines within the function.