Question

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.

Answer 1

correct.

Answer 2

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

Answer 3

sorry, x = 1/2 not in domain so you are right

Answer 4

Thank you both! I appreciate it. :)