Well what's this thing over here going to be? Well f of C is just a number, it's not a function of x anymore, it's just f of C is going to evaluate to something. So this is just going to be f of C. This is just going to be f of C. So if the limit of f of x as x approaches C minus f of C is equal to zero. Well just add f of C to both sides and what do you get? Well you get the limit as x approaches C of f of x is equal to f of C. And this is the definition of continuity, the limit of my function as x approaches C is equal to the function, is equal to the value of the function at C. This is, this means that our function is continuous. Continuous at C. So just a reminder, we started assuming f differentiable at C, we use that fact to evaluate this limit right over here, which we got to be equal to zero. And if that limit is equal to zero, then it just follows, just doing a little bit of algebra and using properties of limits, that the limit as x approaches C of f of x is equal to f of C. And that's our definition of being continuous, continuous at the point C. So hopefully that satisfies you.