Posted by Tyler on Saturday, April 28, 2012 at 10:26pm.
I read you equation as
f(x) = sin (πx)
f'(x) = πcos(πx)
for local max/min, f'(x) = 0
cos(πx) = 0
πx = -π/2 or πx = π/2 or πx= 3π/2
x = ± 1/2 or x = 3/2 , but our domain is [-1,2]
so x = -1/2 or x = 1/2
so
f(-1/2) = sin (-π/2) = -1
f(1/2) = sin (π/2) = 1
also look at endpoints of domain
f(-1) = sin(-π) = 0
f(2) = sin(2π) = 0
so the max is 1 and the min is -1
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