Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.)

g(θ) = 8θ − 2 tan θ

Answer 1

@ganeshie8

Answer 2

Hi?

Answer 3

critical points are the points where
1. function is not defined or
2. derivative of function is zero or
3. derivative of function is not defined

Answer 4

Yes, but im confused on how to work it.

Answer 5

function is defined for all values.
g'(θ) = 8 - 2 sec^2 θ
0 = 8 - 2 sec^2 θ
2 sec^2 θ = 8
sec^2 θ = 4
secθ = 2 or secθ = -2
=> θ = n(pi) + 60degrees or θ = n(pi) - 60degress

Answer 6

understood till there?

Answer 7

Yes

Answer 8

So, g'(θ) becomes zero at those values...Now see where the g'(θ) is not defined.
It is not defined when sec^2 θ is not defined
And, sec^2 θ is not defined at θ = (2n+1)pi/2

Answer 9

So, all those values of θ are called critical points

Answer 10

got it?

Answer 11

I see that... So there it is undefined at both (2n+1)pi/2 and 2n-1)pi/2?

Answer 12

take only (2n+1)pi/2 or (2n-1)pi/2..only one of them and put n = any integer...

Answer 13

So they are both similar?

Answer 14

Yes..they are same for different values of n

Answer 15

Okay thank you.

Answer 16

welcome:)