Quandaries
and Queries 

Hi, I was given the following problem and I tried equating the derivates but then I didnt know what to do from there. Problem: The xaxis is a common tangent of y = x^{2} and y = x^{3}. Find the equation of another common tangent. Shanup 

Hi Shanup, You have two different curves and a common tangent line L. I drew such a diagram below with L tangent to y = x^{2} at x = a and L tangent to y = x^{3} at x = b. Find the slope of the tangent line to y = x^{2} at x = a and the slope of the tangent line to y = x^{3} at x = b. Equate these two expressions to get an equation relating a to b. Find the equation of the tangent line to y = x^{2} at x = a and the equation of the tangent line to y = x^{3} at x = b. These two expressions describe the same line so the yintercepts must be the same. Equate the two expressions for the yintercepts and you have another equation relating a to b. Solve the two equations for a and b. Penny 

