Find the critical numbers of a function

[Permanence]

Thank you for viewing my thread. The following is a problem from my homework that is submitted online. I have already exhausted my attempts, but I'm curious as to where I went wrong. I would appreciate if someone could lead me towards the solution.

Homework Statement

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) = 28θ − 7 tan θ

Homework Equations

The critical values of a function, f, are located where f'(c) = 0 or DNE.

The Attempt at a Solution

g(θ) = 28θ − 7 tan θ
g'(θ) = 28 − 7 sec(θ)^2
0 = 4 - sec(θ)^2
4 = sec(θ)^2, when θ = ((6*n-1)*pi) / 3

 

[STEMucator]

Thank you for viewing my thread. The following is a problem from my homework that is submitted online. I have already exhausted my attempts, but I'm curious as to where I went wrong. I would appreciate if someone could lead me towards the solution.

Homework Statement

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) = 28θ − 7 tan θ

Homework Equations

The critical values of a function, f, are located where f'(c) = 0 or DNE.

The Attempt at a Solution

g(θ) = 28θ − 7 tan θ
g'(θ) = 28 − 7 sec(θ)^2
0 = 4 - sec(θ)^2
4 = sec(θ)^2, when θ = ((6*n-1)*pi) / 3

You have the right idea. Use an identity you know to help you:

$±2 = sec(θ)$
$±2cos(θ) = 1$
$cos(θ) = ±\frac{1}{2}$

Now solve for $θ$.

 

[LCKurtz]

Thank you for viewing my thread. The following is a problem from my homework that is submitted online. I have already exhausted my attempts, but I'm curious as to where I went wrong. I would appreciate if someone could lead me towards the solution.

Homework Statement

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) = 28θ − 7 tan θ

Homework Equations

The critical values of a function, f, are located where f'(c) = 0 or DNE.

The Attempt at a Solution

g(θ) = 28θ − 7 tan θ
g'(θ) = 28 − 7 sec(θ)^2
0 = 4 - sec(θ)^2
4 = sec(θ)^2, when θ = ((6*n-1)*pi) / 3

That is the same as $2n\pi - \frac \pi 3$. I don't think you have all of them.