I need to find a maximum of the function
$$y=\arccos\left(\frac{29+12x\sin(22)+6x\cos(22)+x^2} {\sqrt{x^2+6x\cos(22)-20x\sin(22)+109}\sqrt{x^2+6x\cos(22)-4x\sin(22)+13)}} \right) $$
between x=0 and x=5.
However, WolframAlpha cannot find it and I haven't got access to a more sophisticated software solution e.g. Matlab or Mathematica. Can anybody help me?
Just plot, and it and you'll see there is only one maximum in $[0,5]$
I guess if you take the derivative you will find that there is only a possible stationary point, and then checking the second derivative you would certify it is a maximum. But I guess in that interval the function is even strictly concave.