Locate the absolute extrema of the function f(x)=Sinpix on the closed interval [1,1/3]

Answer 1

y = sin (pi x)
graph it

sin pi = 0
if you go around counterclockwise
where is sin pi x= -1?
where pi x = 3 pi/2 sin ( pi x ) = -1
so min when x = 3/2
we never get to x = 1/2 so max at pi/3
when sin pi x = sin 60 deg = sqrt 3/2