Consider the function defined by
Find values for the constants and such that the derivative exists.
We know that the derivative exists if and only if
exists. Furthermore, this limit exists if and only if the one-sided limits both exist and are equal:
So, plugging in the formula for (which is if we approach from the right, and is if we approach from the left, and noting that from the definition of ) we have,
For the limit on the left to exist we must have (otherwise the limit will diverge as ). Furthermore, this limit must be 0 since is a constant (and the limit of as is 0). Therefore, we have , and we have the equation
Therefore, and are the values of the requested constants in terms of .