Posted by Mary on Saturday, March 9, 2013 at 2:46pm.
Find the minimum and maximum values of the function f(x)= 2/3 sin pix on the interval [1,2] (domain).
I got (1.5, 2/3) as the minimum and no maximum on the interval. Is it correct? Thank you.

Absolute Extrema  bobpursley, Saturday, March 9, 2013 at 2:56pm
correct.

Absolute Extrema  Damon, Saturday, March 9, 2013 at 2:58pm
I bet you mean
f(x) = (2/3) sin(pi x)
f'(x) = (2/3) pi cos(pi x)
f'(x) = 0 for max or min
that is when cos (pi x) = 0
x = 1/2 and x = 3/2
if x = 1/2
y = (2/3)sin (pi/2) = 2/3
if x = 3/2
y = (2/3) sin (3 pi/2) = 2/3
PS
You can be sure that the max and min of a sin function are +1 and 1

Absolute Extrema  Damon, Saturday, March 9, 2013 at 3:00pm
sorry, x = 1/2 not in domain so you are right

Absolute Extrema  Mary, Saturday, March 9, 2013 at 3:20pm
Thank you both! I appreciate it. :)
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