Maxima and Minima of tan(sinx + sin3x) on (-pi,pi)

  • Thread starter wildcat12
  • Start date
  • Tags
    Max
In summary, the conversation discusses finding the maxima and minima of the function f(x)=tan(sinx + sin3x) on the interval (-pi,pi), with a focus on finding critical points using the derivative. The correct derivative is given by \frac{\cos(x)+3\cos(3x)}{\cos^2(\sin(x)+\sin(3x))}, leading to the equation \cos(x)=-3\cos(3x) which has infinitely many solutions.
  • #1
wildcat12
9
0

Homework Statement


Find the maxima and minima of the function f(x)=tan(sinx + sin3x) on the interval (-pi,pi)


Homework Equations





The Attempt at a Solution


I found the derivative as sec^2x (sinx +sin3x) (cosx + cos3x) and when i set it equal to zero i found critical points at Sin=pi/2, and cos=pi/2
 
Physics news on Phys.org
  • #2
Your derivative is incorrect. The derivative of sin(3x) is not cos(3x)...
 
  • #3
Wait i typed that part wrong. i had derivative of sin(3x) as 3Cos(3x)
 
  • #4
Good, so your derivative is

[tex]\frac{\cos(x)+3\cos(3x)}{\cos^2(\sin(x)+\sin(3x))}[/tex]

This can only become zero if [tex]\cos(x)+3\cos(3x)[/tex]. So you'll need to solve the equation [tex]\cos(x)=-3\cos(3x)[/tex]. I believe there will be infinitly many solutions to this, but I'm not sure...
 

FAQ: Maxima and Minima of tan(sinx + sin3x) on (-pi,pi)

1. What is the purpose of finding max and min values in scientific research?

Finding the maximum and minimum values in a dataset is crucial for understanding the range and variability of the data. This information can help identify outliers, trends, and patterns in the data, which can then inform further analysis and conclusions.

2. How do you determine the maximum and minimum values in a dataset?

To determine the maximum and minimum values in a dataset, you can either manually scan through the data or use statistical software. The most common method is to use the "max" and "min" functions, which will automatically calculate and display the highest and lowest values in the dataset.

3. Can the maximum and minimum values change if new data is added to the dataset?

Yes, the maximum and minimum values can change if new data is added to the dataset. This is because the addition of new data can alter the range and distribution of the data, potentially affecting the maximum and minimum values.

4. What do outliers in the data indicate about the maximum and minimum values?

Outliers are data points that are significantly different from the rest of the dataset. They can affect the maximum and minimum values, potentially skewing the results. It is important to identify and analyze outliers separately to determine if they are genuine data points or errors.

5. How do you interpret the maximum and minimum values in relation to the rest of the data?

The maximum and minimum values provide important context for understanding the distribution of the data. They can help identify the range of values that the data falls within and whether the data is evenly or unevenly distributed. Additionally, comparing the maximum and minimum values to the mean and median can provide insights into the overall shape of the data.

Similar threads

Back
Top