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Find the critical numbers of a function

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  • #1
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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
f2acfb64dbc9f8b72b5f9d2c6e6b696f.png

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

74a99371c78723958c43625d14b4e2e6.png
 

Answers and Replies

  • #2
STEMucator
Homework Helper
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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
f2acfb64dbc9f8b72b5f9d2c6e6b696f.png

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

74a99371c78723958c43625d14b4e2e6.png
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##.
 
  • #3
LCKurtz
Science Advisor
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Gold Member
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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
f2acfb64dbc9f8b72b5f9d2c6e6b696f.png

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.
 

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