How do you know if a point is not differentiable?

If there derivative can’t be found, or if it’s undefined, then the function isn’t differentiable there. So, for example, if the function has an infinitely steep slope at a particular point, and therefore a vertical tangent line there, then the derivative at that point is undefined.

Why is x2 not differentiable?

Also for this function √|x−2|, the right hand limit at x=2 and left hand limit at x=2 does not match, so limit doesn’t exist at x=2, hence not differentiable.

How do you check whether the function is differentiable or not?

A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean? It means that a function is differentiable everywhere its derivative is defined. So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable.

What makes a point differentiable?

Hence, differentiability is when the slope of the tangent line equals the limit of the function at a given point. This directly suggests that for a function to be differentiable, it must be continuous, and its derivative must be continuous as well. Thus, a differentiable function is also a continuous function.

Where is f differentiable?

Is a corner differentiable?

A function is not differentiable at a if its graph has a corner or kink at a. Since the function does not approach the same tangent line at the corner from the left- and right-hand sides, the function is not differentiable at that point.

Is a hole differentiable?

Using that definition, your function with “holes” won’t be differentiable because f(5) = 5 and for h ≠ 0, which obviously diverges. This is because your secant lines have one endpoint “stuck inside the hole” and thus they will become more and more “vertical” as the other endpoint approaches 5.