Maximum and chnage of sign of a function

In summary, the person is asking for help in finding a function (either cosine or sine) that has a maximum at 7Pi/4 and at the same time changes sign under phi->phi+Pi with 0< phi< 2Pi. They mention knowing how to shift and stretch functions and someone else suggests using a function like sin(x+pi)=-sin(x) but the person clarifies that the maximum of the function should be at phi=7Pi/4. They suggest using the function sin(phi-pi/4).
  • #1
Physicslad78
47
0
Guys Can anyone help me in this? I need a function (cos or sin) maximum at 7Pi/4 and at the same time changes sign under phi->phi+Pi with 0< phi< 2Pi...Thank you
 
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  • #2
Do you know how to shift and stretch functions?
 
  • #3
Yes of course I do and u can find a function that is maximum at 7pi/4 but the problem is how to also make it change sign under phi->phi+Pi...
 
  • #4
[tex]sin(x+ \pi)= -sin(x)[/tex]

That's no problem at all!
 
  • #5
Thanks HallsofIvy but the maximum of the function should be at [tex] \phi=\frac{7\pi}{4}[/tex]. I guess the function should be [tex] \sin (\phi-\frac{\pi}{4}) [/tex]
 

1. What does the maximum of a function represent?

The maximum of a function represents the highest point on the graph of the function, where the output value is the largest.

2. How can I find the maximum of a function?

To find the maximum of a function, you can use calculus techniques such as taking the derivative and setting it equal to zero, or finding the critical points and evaluating the function at those points.

3. What does the change of sign of a function indicate?

The change of sign of a function indicates a change in the direction of the graph, from increasing to decreasing or vice versa. It can also represent a change in the nature of the function, such as from concave up to concave down or vice versa.

4. How can I determine the change of sign of a function?

To determine the change of sign of a function, you can analyze the intervals where the function is positive and negative, or use the intermediate value theorem to find where the function crosses the x-axis.

5. Can a function have multiple maximum points?

Yes, a function can have multiple maximum points if the graph has multiple humps or peaks. In this case, each maximum point would represent a local maximum, as opposed to a global maximum which is the absolute highest point on the graph.

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