In the solution to problem 1.1.11, there's is one line in the solution that is giving me trouble. Here is the problem:

Suppose that is a twice differentiable real function such that for all . Find all real numbers at which the area between the graph , the tangent to the graph at , and the lines , attains its minimum value.

At some point we need to differentiate (with respect to c)

and get

,

but I'm getting other things which don't allow successful solution to the problem (my expression for doesn't have a in it).

Can someone explain?