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I found the slope of the graph by using the chain rule and found that dy/dx=−tan(θ)

and the concavity d2y/dx2=2(tanθ)^3/2

This is a pretty messy derivative so I checked it with wolfram alpha and both functions are correct (but feel free to check in case I made a mistake that would explain this all).

My problem is that the concavity function indicates that it will never be concave down and always concave up but if you graph the function it looks like a typical 1/x function, which means IT IS concave down in Q3.

I found this extremely interesting and it's killing to figure out why, is it because my concavity function is in terms of theta? or perhaps was there a +/- or something?

If someone can shine some light as to why it's like this or push me in the right direction, it'd be greatly appreciated.