Find the minimum distance between the curves y=e^x and y=lnx. Hint: Use the fact that e^x and lnx are inverse relationships. I have no idea where to start. Thanks!

Answer 1

to get you going:

let P(a , e^a) and Q(b, lnb) be the closest points on their respective graphs

since they are inverses the line PQ must be perpendicular to y = x
but y = x has a slope of 1, so the
sope of PQ = -1

See what you can do with that.