Hi, we just finished talking about relativity in my physics class, and using its equations we were supposed to find a fuel efficient speed limit for our highways if the speed of light were 30m/s. This course assumes no calculus, but since i know some differential calculus I get the feeling calculus can help. I'm considering a graph of mass versus x where x=v/c where v=object's velocity and c= speed of light using the function m(x)=(1-x^2)^(-1/2) I get the graph shown, and I am wondering if the point where the derivative is 1 would be what I'm looking for. I say this because before that the mass is increasing pretty slowly,and then after that the mass increases drastically while the velocity does not increase much. Secondly if the graph were rotated as shown, the tangent line I'm considering would be horizontal, ie a critical point. The course isn't calculus based, and I think we were just supposed to estimate, or something obvious is slipping by me, but I'd just like to know what anyone thinks. My math teachers told me to try a forum since they don't really know...my physics teacher, although quite good, is not well versed in calculus and can just agree that generally what I'm saying makes sense. I was hoping someone here might be able to give me a hand in this, and if I'm being vague in the problem let me know I'll try and explain myself better. For the record, the extent of my calculus knowledge is basic differential calculus thanks to our awesome ministry of education. So far I've differentiated the equation and solved for f'(x)=1,and I got a value somewhere in the neighbourhood of x=0.5 (I don't remember exactly and don't have my work with me right now), which seems like a reasonable value. Thanks in advance for any insights.