Determine all real values of a and b such that the function
f(x) = ax+b for x =< 1
= tan(Pi*x/4) for 1 < x < 2
is differentiable at x = 1
Is this the correct function?
You basically need to check for two things:
1) The function must be equal on both sides as
2) The function's derivative must be equal on both sides as
For the first condition, plug in into both parts to get:
And the second condition, take derivatives of both sides, then plug in to get:
Once you have established these two equalities, you can now determine what are.