I am trying to solve the problem of finding a point, which minimizes the time required to move from some point to another, some of the time swimming, some running, anyways in order to do that i have to minimize the function:
$$f(x)=\frac{(x^2+c^2)^{1/2}}{a}+\frac{((x-d)^2+(c-e)^2)^{1/2}}{b},$$
which unfortunately leads to very ugly things, when taking derivative. Is there another, maybe tricky way of finding minimum of this function?