Answer
Parallel to each other.
Work Step by Step
Step 1. Letting $h(x)=f(x)-g(x)$, since point $c$ gives the maximum of $h(x)$, we have $h'(c)=0$
Step 2. With $h'(x)=f'(x)-g'(x)=$, we have $h'(c)=f'(c)-g'(c)=0$; thus $f'(c)=g'(c)$
Step 3. By definition, $f'(c)$ represents the slope of the tangent line to $f(x)$ at point $c$, and the same for $g'(c)$. Thus, we conclude that the tangents to the two curves at $c$ are parallel to each other.
