for what values of a and c is the function f(x)=
ax^2, x is less than or equal to 2
x+c, x is greater than 2
differentiable for all real values of x?
i did the limit from each side and got the equation 4a= 2+c
but how do i make another equation? thanks!
Edit: Uh, oh. I had a problem like this a few weeks ago, and solved it the way I typed it up above. I got it right, but I now realize that was just a happy accident. Now I know better.
Note that the fact that if a function is differentiable at x= a, the derivative is not necessarily continuous there. However, it is always true that the derivative has the "intermediate value property" so that the two one sided limits, if they exist, must be the same.