1. The problem statement, all variables and given/known data Let f(x) = axe^((bx)^2). Find the value for a times b if it's known that there's a max value of 2 at x = 3. Second, There is one line which is tangent to the curve y = 1/x, at some point A and at the same time tangent to the curve x^2 at some point B. What is the distance between A and B? 2. Relevant equations For the first I realize that I have f'(3) = 0 and (I think) f(3) = 2. Second, I think I can set the derivatives equal to each other and solve for x. 3. The attempt at a solution I can then use these equations to solve for a and b, however I guess this is more an algebra problem because I seem unable to do so. I also need verification that that second equation makes sense. If it does, I think I'll be more able to do this question because I can solve for b in a way I couldn't with the first equation (if I took ln of both sides ln0 would be undefined and it wouldn't make sense, I think). Second, when I tried to solve for x I ended up with x = 1/2 which lead me to a solution eventually, by the distance formula, of 9/16 + 1/16 which is not correct based on the test answers. Any help would be appreciated here, thanks guys!