f(x)= sinx-cosx+2^1/2 whole divided by x^3/2 where x belongs to[Π/4,5Π/4].let m the minimum value of f(x) and M be the max value of f(x).then [2M/5m] where [.] denotes greatest integer function
The given expression is
S = [√2*sin(x-Π/4) + √2] / x3/2 = √2 [sin(x-Π/4) + 1] / x3/2
Note that (x-Π/4) ε [0,Π].
So clearly S is maximum when x=Π/4, and minimum when x=5Π/4.
So now you can find what [2M/5m] will be.