Three Conditions for Differentiablity

[Jason76]

In order for a function to be differentiable:

1. It must be continuous

hint on other two?

 

[pka]

In order for a function to be differentiable:

1. It must be continuous

hint on other two?

What other two?

 

[Jason76]

Actually, the problem states:

State the three cases where a function is not differentiable

1. The limit of the difference quotient exists.

2. Where it has no left hand or right hand derivative.

3. Where there is a missing point that is not defined.

4 (extra) corners of the absolute value function

5. (extra) vertical tangents of cubed root function

6. (extra) A hyperbola with a vertical tangent.

 

[stapel]

Actually, the problem states:

State the three cases where a function is not differentiable

1. The limit of the difference quotient exists.

Is this part of your answer? Part of the exercise? Part of another exercise? Something else?

If this is part of your answer, by what reasoning did you conclude that a function is NOT differentiable at a point for which the limit exists?

 

[Jason76]

My professor gave the following as answer.

A function is NOT differentiable at:

1. a corner

2. a discontinuity

3. A vertical tangent line

 

[daon2]

what is the class that you are taking that the professor used the term "a corner" ?

all of these 3 are just places where the limit that is the definition of the derivative of a function at a point doesn't exist.

Calculus texts refer to the graph of function f(x) as having "corners" or "sharp points" at x=a when f(x) is differentiable for x satisfying 0<|x-a|<delta for some delta, and continuous at x=a, but f'(a) is not defined.