Finding 'k' for Continuous f(x) at x=2

[ashleyk]

Let f(x) be a function defined by:

f(x)= { 2x+1 for x (less than or equal to) 2
.5x + k for x (greater than) 2

A) For what value of 'k' will f(x) be continuous at x=2? Justify your answer.
B) Using the value of 'k' found in part A, determine whether f(x) is differentiable at x=2.


Any help on where to get started would be great. I think I have to plug in the 2 in the first equation...but I'm lost on what to do. Thanks.

 

[Hurkyl]

The definitions are usually a good place to start when you don't know what to do. What does it mean for this particular function to be continuous at 2?

 

[mathwonk]

and remember to think about both right and left hand limits in defining continutity.

 

[dextercioby]

And remember to make the distinction between right and left when discussing differentiability...

I think you got enough clues...

Daniel.