Critical Numbers for f(x)=2sin(2x)/x on [-pi,pi]

  • Thread starter cdhotfire
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In summary, the conversation is about an equation, f(x)=\frac{2\sin{2x}}{x} [-\pi,\pi], and the process of finding its critical numbers. The first derivative, f'(x)=\frac{2(2x\cos{2x} - \sin{2x})}{x^2}, is set equal to 0, but the speaker is having trouble finding the critical numbers and has tried using double angle without success. They have also posted about this in a different section and are waiting for a response.
  • #1
cdhotfire
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Well, I got this equation [itex]f(x)=\frac{2\sin{2x}}{x}[/itex] [itex] [-\pi,\pi][/itex]
So I took the 1st derivative, [itex]f'(x)=\frac{2(2x\cos{2x} - \sin{2x})}{x^2}[/itex]
Then I set that equal to 0, and got [itex]0=2x\cos{2x} - \sin{2x}[/itex]
But I do not see how to get the critical numbers, I also tried to do double angle, but that just resulted in more pain.:mad:
Any help, would be appreciated.:smile:
 
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  • #2
Please.:rolleyes:
 
  • #3
Haven't I seen this somewhere before? :)
 
  • #4
Tide said:
Haven't I seen this somewhere before? :)

ya, i know, i though no one visited the mathematics section, because i was only able to join it by using the search tool. Also, i put a note for someone to delete my post in the other section.:smile:

btw, i posted back on you reply.:-p
 

FAQ: Critical Numbers for f(x)=2sin(2x)/x on [-pi,pi]

What is the definition of a critical number?

A critical number is a point on a function where the derivative is equal to zero or does not exist. It is also known as a stationary point or turning point.

Why is finding critical numbers important?

Finding critical numbers allows us to identify important information about a function, such as its local extrema (maximum and minimum values), points of inflection, and intervals of increasing or decreasing behavior. This information can help us analyze and understand the behavior of the function.

How do you find critical numbers?

To find critical numbers, we first take the derivative of the function and then set it equal to zero. We then solve for the variable to find the x-values where the derivative is equal to zero. These x-values are the critical numbers of the function.

Can a function have more than one critical number?

Yes, a function can have more than one critical number. In fact, a function can have multiple critical numbers within a given interval, depending on the complexity of the function.

Are all critical numbers considered local extrema?

No, not all critical numbers are considered local extrema. A critical number can be a point of inflection or a point of horizontal tangent, which are not considered local extrema. Only critical numbers that occur at the highest or lowest points of a function are considered local extrema.

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