Question

Consider the function on the interval (0, 2π).
x/2 +sin(x)

Apply the First Derivative Test to identify the relative extrema.
relative maximum (x, y)=


relative minimum (x, y) =

I believe the derivative is 1/2 -cos(x), but i don't know how to find the max or min. i found the critical numbers: pi/3 & 5pi/3
Please help

Answer 1

you got the derivative?

Answer 2

oh yeah,i see that you do have it, but a slight mistake
it should be
\[\large f'(x)=\frac{1}{2}\color{red}+\cos(x)\]

Answer 3

if you set that equal to zero and solve, you get
\[\cos(x)=-\frac{1}{2}\] so
\[x=\frac{2\pi}{3},\frac{4\pi}{3}\]

Answer 4

the first is a local max, the second is a local min

Answer 5

@satellite73 that's all? how to find y? would y be 0?

Answer 6

way beyond my level...