True or false about a statement considering continuity and the derivative.

Question

If f'(a) is defined, then f(x) is continuous at x=a.

 

True or False? I'm not exactly sure what this means. Isn't f'(a) the tangent slope? and since there can only be one it can't be continuous so this statement is invalid all together?

Please help me, I still don't understand these concepts very well...

Answer 1

I withdraw this answer due to an error on my part.  Mark's answer below is correct.

Answer 2

"f'(a) is defined" means that f(x) is differentiable at x = a (in other words, the derivative exists when x = a).  If a function is differentiable at a point then it must automatically be continuous at that point as well.  

 

So, the answer to the given question is:  TRUE.