Hello gwtkof

Welcome to Math Help Forum!I think you will need to use a numerical/graphical method to solve this.

The second point of intersection will be when the line is a tangent to the curve between and .

Using an Excel spreadsheet, I set up graphs of the two functions, and found, by a series of approximations, this to be when , with .

Grandad

PS

A more analytical approach is to say that the gradient of at the point when it touches the line will be . So if you solve the equations

andsimultaneously, you'll end up with

which will again require a numerical method.

This gives the same approximate values as I stated above.