Given f′(sinx)<0 and f′′(sinx)>0 for all x∈[0, 5/2], what can be concluded about the function f(x)?

a) f(x) is increasing on the interval [0, 5/2]
b) f(x) is decreasing on the interval [0, 5/2]
c) f(x) has a local minimum at x= π/2
d) f(x) has a local maximum at x= π/2