Hello, Rumor!

IthinkI have a solution.

Please check my reasoning and my work.

We have: .If , the graphs of: and intersect for

Find the smallest value of for which the graphs are tangent.

What are the coordinates of the point of tangency?

The graphs intersect at the point of tangency.

. . Hence: . [1]

Their slopes are equal at the point of tangency.

. . Hence: . [2]

Divide [1] by [2]: .

We have: .

Since , we have: .

Therefore: .

And the point of tangency is: .