1. The problem statement, all variables and given/known data Let f be the function given by f(x) = 3e^2x and let g be the function given by g(x) = 6x^3. At what value of x do the graphs of f and g have parallel tangent lines? a. -0.701 b. -0.567 c. -0.391 d. -0.302 e. -0.258 Correct answer is c. -0.391 2. Relevant equations 3. The attempt at a solution Well, tangent line means doing the derivative. Thus, I did the derivative of f and g. f'(x) = 6e^2x g'(x) = 18x^2 Parallel means the slopes or the derivatives are the same. Thus, I set them equal to each other in order to solve for x. f'(x) = g'(x) 6e^2x = 18x^2 e^2x = 3x^2 Here I was stuck. I could do ln(e^2x) to cancel out the e, but I would end up with something ugly on the right side. 2x = ln(3x^2) and I wouldn't have x on one side. Am I approaching this problem incorrectly, or is my algebra wrong?