When Are Graphs Not Differentiable?

A function is not differentiable at a if its graph has a vertical tangent line

at a. The tangent line to the curve becomes steeper as x approaches a until it becomes a vertical line. Since the slope of a vertical line is undefined, the function is not differentiable in this case.

What makes a graph non differentiable?

A function is non-differentiable where it has a "cusp" or a "corner point". This occurs at a if f'(x) is defined for all x near a (all x in an open interval containing a ) except at a , but limx→a−f'(x)≠limx→a+f'(x) . (Either because they exist but are unequal or because one or both fail to exist.)

How do you know if a graph is differentiable?

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.