Posted by **Ginger** on Monday, December 1, 2008 at 11:17pm.

For a function f(x) the derivative at x=2 is 5. Is the derivative of f(x) continuous at x=2? Thanks!

- calculus -
**drwls**, Monday, December 1, 2008 at 11:25pm
If a function has a derivative at a point, the function must be continuous there.

- calculus -
**Ginger**, Tuesday, December 2, 2008 at 7:34am
Isn't it asking if the derivative is continuous? Not whether the function is continuous?

- calculus -
**drwls**, Tuesday, December 2, 2008 at 8:35am
Yes, I misread the question. My mistake.

According to this reference:

http://www.math.colostate.edu/~reinholz/ed/08fa_m160/lectures/mean_value_theorem.pdf

the existence of a derivative of a function at a point does not necessarily imply that the derivative is continuous. An example is provided of a function with derivatves throughout a region for which the derivative is not continuous at one point in the region.

## Answer This Question

## Related Questions

- Calculus - Explain the global optimization process for a continuous function ...
- Calculus - Explain the global optimization process for a continuous function ...
- Calculus (Global Max) - Explain the global optimization process for a continuous...
- calculus - Find the derivative of the function using the definition of ...
- Calculus - Consider the function f(x) = {0, x = 0 and 1 - x, 0 <= x <= 1...
- Calculus - Hello I need help with this excersise of derivative of a inverse ...
- math - Let f be a real value function and x Î Df then 0 lim ( ) ( ) h f x h f x...
- Calculus - Use a symbolic differentiation utility to find the derivative of the ...
- calculus - You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the...
- Calculus--> bobpursley - How do you get m=0? from taking the second ...

More Related Questions