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 x-axis is a common tangent of y = x2 and y = x3. 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 = x2 at x = a and L tangent to y = x3 at x = b.
Find the slope of the tangent line to y = x2 at x = a and the slope of the tangent line to y = x3 at x = b. Equate these two expressions to get an equation relating a to b.
Find the equation of the tangent line to y = x2 at x = a and the equation of the tangent line to y = x3 at x = b. These two expressions describe the same line so the y-intercepts must be the same. Equate the two expressions for the y-intercepts and you have another equation relating a to b.
Solve the two equations for a and b.
Penny