# Homework Help: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equals c

1. Jan 27, 2013

### tsuwal

1. The problem statement, all variables and given/known data
True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equals c

2. Relevant equations

3. The attempt at a solution
I know that if f'(a) exists the statement is true, but is it true that based on that information f'(a) exists?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 27, 2013

### jbunniii

Re: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equa

Look at the definition of the derivative. $f'(a) = c$ means that
$$\lim_{x \rightarrow a}\frac{f(x) - f(a)}{x - a} = c$$
Try applying the mean value theorem to
$$\frac{f(x) - f(a)}{x - a}$$
and see if you can conclude anything.

3. Jan 27, 2013

### tsuwal

Re: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equa

yes, my teacher explained t that way but the last part of the demonstracion when he uses some theorem about the limit of compound functions with csi(x) is really confusing..

4. Jan 27, 2013

### jbunniii

Re: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equa

Suppose $x > a$. Does the mean value theorem apply to $f$ on the interval $[a, x]$? If so, what does it say?