Equation of tangent lines, find intersection

I am having a bit of an issue with this problem.

f(x) = e^(-cx) and g(x) = -e^(-cx) where c is a positive real number.

"Find equations of the tangent lines to the curves f(x) and g(x) at x = 0. Then show they intersect on the x-axis at the point (1/c, 0)."

Okay so for the tangent lines they want me to take the derivatives of f(x) and g(x) right?

Well here they are:

f'(x) = -ce^(-cx)

g'(x) = ce^(-cx)

f'(0) = -c

g'(0) = c

But these are constants! Just flat horizontal lines that won't intersect because they're parallel. So why is the problem asking me to prove they intersect at (1/c, 0)? I know I did something wrong, but what?

Any hints are much appreciated.