Question

Calculus Help?
Find any critical numbers of the function
h(x)=sin^2(x)+cosx and the limits are 0 13 years ago

Answer 1

I have no idea how to do this after finding the derivative so any help would be great!

Answer 2

critical numbers include when h'(x) =0 and when h''(x) = 0

Answer 3

Are regular zeros also critical numbers? I don't remember...

Answer 4

What did you get for h' ?

Answer 5

yeah I got that part down but how would I exactly use it, the derivative that I got was f'(x) = 2(sinx)(cosx)-(sinx)

Answer 6

ok, set that equal to zero:
0 = 2(sinx)(cosx)-(sinx)

Answer 7

factor out sin(x):
0 = 2(sinx)(cosx)-(sinx)
0 = sin(x)(2cosx - 1)

and solve the two parentheses for zero:
sinx = 0 and 2cosx - 1 = 0

Answer 8

ahh so would I need to take the inverse of sin for sinx = 0 then?

Answer 9

which would equal 0?

Answer 10

Well, yes, but I prefer to look at the unit circle, sinx = 0 at only one place in your domain ...(unless you meant to include 0)...

Answer 11

lol yeah I got it from the unit circle

Answer 12

what did you get?

Answer 13

wait would that be 0? on the unit circle the sin of 0 is 0..?

Answer 14

yes, and also pi. Now solve 2cosx-1 = 0

Answer 15

so that would be cosx =1/2 which would be pi/3

Answer 16

would these values be my answer or would I need to plug them in still to the original equation?

Answer 17

And one more answer for cosx = 1/2

Answer 18

5pi/3

Answer 19

nevermind answered my own question, thanks a lot for guiding me through the problem! :)

Answer 20

Good, those are all the critical numbers in the domain for the first derivative.

Answer 21

thanks I understand them a lot better now