When is a function NOT differentiable? (1 Viewer)

[abdog]

Like the question says, when is a function NOT differentiable?

 

[Leffife]

When a function isn't continuous it cannot be differentiated.

 

[abdog]

what do you mean continuous?

 

[Praer]

y = x for 0 < x < 4
and y = 5 for 6< x <7
something like that

 

[deswa1]

When it is non-continuous (i.e. doesn't exist at that point). Like y=1/x at x=0. Also when things have like a sharp corner- technically when the limit of the gradient is different when you approach from both sides. Like y=|x| at x=0

 

[abdog]

so if it is a straight line it cannot be differentiated? Can you explain with diagrams?

 

[deswa1]

A straight line can be differentiated. Consider the line y=1. This is a horizontal line with constant gradient of 0. The derivative is a function of the gradient at any point on the curve- hence the derivative of a straight line y=k for some constant k is dy/dx=0.

Even other lines, like y=x has a constant gradient of 1, hence dy/dx=1 etc etc.

For curves, you need more than just this constant gradient because the gradient changes- hence the idea behind first principles differentiation

 

[Drewk]

When there is a a sharp corner for instance the tangent to at that point can be drawn with multiple directions/gradients

 

[kaz1]

also when there is a vertical tangent

 

[SpiralFlex]

Discontinuity does not necessarily mean it doesn't exist at that point.

 

[Mr Slick]

Discontinuity does not necessarily mean it doesn't exist at that point.

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