Question

What are the critical numbers of y= sin^2 (x) ?

Answer 1

\[x = π/3, 2π/3, 4π/3, 5π/3\]

Answer 2

but critical numbers in the answer key said pi, pi/2 and 0

Answer 3

its like that only

Answer 4

you should specify an interval. Example from [0, 4\[pi\]

Answer 5

the restriction is -pi < x < pi

Answer 6

srry forgot to type that out

Answer 7

critical numbers are those that make the derivative of the said function zero or makes it undefined

Answer 8

i have trouble with derivative
i got 0 = sin 2x
so does it mean x = 0

Answer 9

then is this 0 for cos or sin..cuz it gives a different value in the unit circle

Answer 10

the derivative of that is 2sinxcosx. but since there are no values that make this undefined just solve it like this 2sinxcosx=0

Answer 11

your critical numbers should be pi, pi/2 and 0

Answer 12

how u get that..?

Answer 13

i got the derivative as 2sinxcosx too..but dont know abt the critical numbers

Answer 14

like I said critical numbers are those that make the derivative of the said function zero or makes it undefined

Answer 15

but since that function can't be undefined for any value of x just solve for x that makes that function equal to zero

Answer 16

dont u use unit circle to find it?

Answer 17

well no. But that's another way to do it

Answer 18

ok thanks!

Answer 19

:D You're welcome!