I've been given a function $$y=\sqrt{2+x^2}-3x$$
and I need to find the absolute minimum and maximum between $[5,6]$. I've already found (assuming I did it right) the derivative of y to be $$f'(x)=\frac{2x}{2\sqrt{x^2+2}}-3$$
Now I need to find the critical values, but I'm not sure if I did something wrong or if I don't know how to do it given this problem. I've come up to a roadblock because I'm dealing with a square root, and I can't get all the x variables to one side, aside from having $$\frac{2x}{2\sqrt{x^2+2}}=3$$ or $$x=3\sqrt{x^2+2}$$
Can somebody point me in the right direction? Thanks.