1. The problem statement, all variables and given/known data Determine the FIRST maximum and minimum values of the underdamped oscillation: y=e^(-x/2)(4sin(3x)+3cos(3x)) cm 2. Relevant equations 3. The attempt at a solution I firstly differentiated the above equation and got: (-e^(-x/2)(22sin(3x)-21cos(3x)))/2 I checked this and it is correct. Next I set this equation to = 0 I crossed off the exponential function (it can't equal 0?) and the /2 on the bottom. 22sin(3x)-21cos(3x)=0 21=22tan(3x) tan(3x)=21/22 tan^(-1)(21/22)=0.7621 I plotted the graph online and checked this point, but it's definitely not a maximum or minimum, so I don't really understand; I thought that I could put dy/dx = 0 and that would tell me the points. Also, this has only given me one point. How will I find the next point? Tan^(-1)(a number) only gives one definitive value. I know that I can take the second derivative and that will tell me if the point is a maximum or minimum (+for minimum,-for maximum). Can anyone help me understand how max and min works for this kind of equation? The oscillation gradually gets smaller, which I haven't ever done before. Thank you!