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.