Question

I'm trying to find critical numbers. The question is find any critical numbers of the function f(theta)=2 sec(theta)+tan(theta)
10 pi 10 years ago

Answer 1

@Sophie_dofi

Answer 2

\[2\sec \theta+\tan \theta \]

Answer 3

??

Answer 4

Yes

Answer 5

so for critical numbers we have the derivative 0 or undefined right?

Answer 6

Yea

Answer 7

I got I know it's something pi/6

Answer 8

\[f'(\theta)=2\sec \theta \tan \theta+\sec ^{2}\theta\]

Answer 9

\[=\sec \theta (2\tan \theta +\sec \theta)\]

Answer 10

Yes I'm past that you end up with 2sin(x)=-1 and sin(x)=-1/2

Answer 11

this expression is undefined or 0...
so solve for sec theta=0 , cos theta=0 and 2tan theta + sec theta=0 or (1/2tan theta +sec theta)=0

Answer 12

but sec theta never equals zero

Answer 13

Is it 67pi/6

Answer 14

71?

Answer 15

cos theta =0 when theta is an odd multiple of pi/2

Answer 16

I don't have a caululator... That's why I'm on here I left it at my moms

Answer 17

wolframalpha.com

Answer 18

Will not calculate equations like this.

Answer 19

10pi < theta < 12 pi
so here the solutions are given by

Answer 20

\[10\pi<(2n+1)(\pi/2) <12\pi \]

Answer 21

from here you will get two vaules of n, which are 10 and 11 ..
so 21pi/2 and 23pi/2 are solution from cos theta=0

Answer 22

next we need to compute the second part

Answer 23

I'm taking notes with this bye I'm not ignoring you thank you very much

Answer 24

*so

Answer 25

and the second part gives us sin x=-1/2

Answer 26

That's where I ended up

Answer 27

in (10pi,12pi) we need the solution

Answer 28

we know that sin 7pi/6 is -1/2

Answer 29

10pi=31.42 and 12pi=37.69

Answer 30

so we need to solve for \[10\pi<n \pi+ (-1)^{n}(7\pi/6)<12\pi\]

Answer 31

And... Now I'm lost

Answer 32

sin x=sin y implies \[x=n \pi+(-1)^{n}y\]

Answer 33

I used this formula

Answer 34

Ok

Answer 35

see n cannot be greater than 12 or else the range goes out of 12pi and also n cannot be less than 10 or else the value will be less than 10pi

Answer 36

check that n=10,11

Answer 37

Oh

Answer 38

so the solutions are 10pi+7pi/6 and 11pi-7pi/6

Answer 39

that is 67/6pi and 59/6pi

Answer 40

so the final solutions are 21pi/2, 23pi/2, 59pi/6 and 67pi/6

Answer 41

lovely only 67pi/6 is an option

Answer 42

Whohoo!

Answer 43

ok then this is the solution.:)

Answer 44

Thank you soooo much! Math is not my forte!

Answer 45

do you understand the method???

Answer 46

I have it all written down so I'll be able to try it again. I think I understand

Answer 47

It's much easier with my caululator

Answer 48

yes only if the calculator is allowed..:)

Answer 49

My teacher allows it, we're a small class and were at the lowest level of calc available. She knows we won't ever go into a field with it or anything. As long as we understand the importance of learning ext.