Question

f(x)=x+cosx on [-2π,2π] how to find the critical numbers

Answer 1

First find the derivative

Answer 2

well ya its 1-sinx

Answer 3

Good. Now find when the derivative equals 0. This is a bit trickier

Answer 4

i know the answer is -3/2pi and pi/2 but i have no idea why

Answer 5

so

1-sinx=0
sinx = 1

Look at the unit circle. When does sin = 1?

Answer 6

sin means the y-coordinate of the angle btw

Answer 7

2pi?

Answer 8

no i mean pi/2

Answer 9

oh its also -3/2pi cus on the unit circle -1 is 3/2pi....so you just do the opposite right?

Answer 10

No you explained it wrong. That's just a coincidence. sin(pi/2) = 1, for sure. Now the range is [-2π,2π] so it menas you can go clockwise or anti-clockwise from 0. If you go counterclockwise you get pi/2. If you go clockwise, you get to -3pi/2.