# Find the critical numbers of a function

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

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STEMucator
Homework Helper
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
Homework Helper
Gold Member
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.