I'm trying to find the global minimum on $$\cos x+\cos kx$$ with $k$ irrational.
The fact that the function oscillates fairly quickly makes it pretty unreasonable to compute the derivative and set it equal to zero (I haven't been able to solve $-\sin x-\sin kx=0$ analytically or numerically anyways), and the local minimums are reasonably close making it hard to tell from the graph.
I tried using Mathematica's NDSolve function to no avail, and every time I broaden the range on FindMinimum I get a different result!
Edit: If there is no global minimum, is there a way to generate the local minima?
Any suggestions about numerically, graphically or analytically solving this problem would be welcome!