How do you determine the five critical points of f(x) = 3cos2(x - π) + 1?

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Bilal7

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How do you determine the five critical points of f(x) = 3cos2(x - π/4) + 1?

How do you determine the five critical points of f(x) = 3cos2(x - π/4) + 1?

I need the critical points for its first cycle. I need help on this question urgently, lots of thanks for whoever answers. :D
 
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Do you not know what "critical point" means? If so I would think you could look it up in whatever text or chapter you found this problem.
 
Take a derivative of f(x). solve the equation f'(x) = 0 for x. you may choose first 5 solutions.
 
My textbook doesn't give a clear cut method of how to find the critical points which is why I'm here.
 
definition: a value c in the domain of a function f is called a critical point of f if f'(c)=0 or f'(c) is undefined.
in your case f'(x) is well defined, you only have to do is solve f'(x) = 0 for x.
 
Bilal7 said:
My textbook doesn't give a clear cut method of how to find the critical points
Click to expand...

I'm not sure what you're saying, above, as you wrote "the critical points" (i.e., you used the definite article).

Are you trying to tell us that your text does not cover differentiation of trigonometric functions?

Or, are you saying that your text does not cover how to solve a trigonometric equation? (This would make sense, as you would need a trigonometry text for that.)

What have you done so far? Where exactly are you stuck? :???:

Please read the forum guidelines, before you reply. Here is a link to the summary page; there are links to the complete guidelines, as well as the forum rules, near the bottom of the page.

Thank you.
 
JohnZ said:
definition: a value c in the domain of a function f is called a critical point of f if f'(c)=0 or f'(c) is undefined.
in your case f'(x) is well defined, you only have to do is solve f'(x) = 0 for x.
Click to expand...

Sorry for the late reply people, this is the part that I'm stuck on. This is more or less the definition provided in the book but they don't have any examples of how they got the critical points.

However I tried doing it and this is what I've got so far:

for n = 0, x = pi/4
for n = 1, x = 3pi/4
for n = 2, x = 5pi/4
for n = 3, x = 7pi/4

Can I just use any value for 'n' to find the final point?

 
you did it ! i guess any number will be fine. in description of the problem there is no requirement for which "n" should be.
 
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