Question

a little help with a 1st derivative test problem with trig would make my day (:

Answer 1

did you give me the warning?

Answer 2

I think x is 0 to pi, so the interval can't go to infinity

Answer 3

like this

[pi/6,pi) ?

Answer 4

its not correct

Answer 5

for part b there needs to be one more endpoint :P

Answer 6

I assume you found the first derivative, to look for critical points (turning points) ?
and then set to 0

you should get
8 - 16 cos(2x) =0

Answer 7

i got that

Answer 8

if you simplify that you get
cos(2x)= 0.5

if x goes between 0 and pi, 2x goes from 0 to 2pi
so 2x= 60º or 2x= 300º (but in radians)

Answer 9

so one critical point is at 2x=60 --> x=30º, which is pi/6 radians
the other is at 300/2= 150º, which is 5pi/6 radians

Answer 10

ok i got [pi/6,5pi/6] for the first one and [0,pi/6]U[5pi/6,pi] for the last.. thanks!