Understanding Continuous Functions: Examining f'(7) Undefined

[bearn]

Suppose f is a function such that f'(7) is undefined. Which of the following statements is always true? (Give evidences that supports your answer, then explain how those evidences supports your answer)

a. f must be continuous at x = 7.
b. f is definitely not continuous at x = 7.
c. There is not enough information to determine whether or not f is continuous at x = 7.

 

[topsquark]

Can you think of a function f(x) where the derivative does not exist at x = 7 but is continuous there?

-Dan

 

[bearn]

Can you think of a function f(x) where the derivative does not exist at x = 7 but is continuous there?

-Dan

No,

 

[topsquark]

How about f(x) = |x - 7|?

-Dan

 

[bearn]

Oh, so the answer is a. f must be continuous at x=7?​

 

[topsquark]

Oh, so the answer is a. f must be continuous at x=7?​

Can you think of a function f(x) that has no derivative at x = 7 and is not continuous there?

-Dan

 

[bearn]

I don't think there is

 

[topsquark]

I don't think there is

What about [math]f(x) = \dfrac{1}{x - 7}[/math]?

-Dan

 

[bearn]

What about [math]f(x) = \dfrac{1}{x - 7}[/math]?

-Dan

The answer should be C. then

 

[topsquark]

The answer should be C. then

Yes.

-Dan