I really don't understand how to even begin this problem...otherwise I'd show my attempt. But I've just been staring at it unable to figure it out at all.
All I have figured out thus far is that the equation for intersection is just sinx = ke^-x
Problem: If , the graphs of y = sinx and y = ke^-x intersect for . Find the smallest value for k for which the graphs are tangent. What are the exact coordinates of the point of tangency? [Hint: you should have two equations involving x and k, one for intersection, and one for tangency. It will be difficult to deal with either of these equations separately, but you should be able to figure out the answer by combining them.]
Thank you in advance!